diff --git a/backon/src/backoff/constant.rs b/backon/src/backoff/constant.rs
index 39aa918..9f3f308 100644
--- a/backon/src/backoff/constant.rs
+++ b/backon/src/backoff/constant.rs
@@ -68,6 +68,16 @@ impl ConstantBuilder {
         self.jitter = true;
         self
     }
+
+    /// Set no max times for the backoff.
+    ///
+    /// The backoff will not stop by itself.
+    ///
+    /// _The backoff could stop reaching `usize::MAX` attempts but this is **unrealistic**._
+    pub fn without_max_times(mut self) -> Self {
+        self.max_times = None;
+        self
+    }
 }
 
 impl BackoffBuilder for ConstantBuilder {
@@ -139,32 +149,32 @@ mod tests {
 
     #[test]
     fn test_constant_default() {
-        let mut exp = ConstantBuilder::default().build();
+        let mut it = ConstantBuilder::default().build();
 
-        assert_eq!(Some(Duration::from_secs(1)), exp.next());
-        assert_eq!(Some(Duration::from_secs(1)), exp.next());
-        assert_eq!(Some(Duration::from_secs(1)), exp.next());
-        assert_eq!(None, exp.next());
+        assert_eq!(Some(Duration::from_secs(1)), it.next());
+        assert_eq!(Some(Duration::from_secs(1)), it.next());
+        assert_eq!(Some(Duration::from_secs(1)), it.next());
+        assert_eq!(None, it.next());
     }
 
     #[test]
     fn test_constant_with_delay() {
-        let mut exp = ConstantBuilder::default()
+        let mut it = ConstantBuilder::default()
             .with_delay(Duration::from_secs(2))
             .build();
 
-        assert_eq!(Some(Duration::from_secs(2)), exp.next());
-        assert_eq!(Some(Duration::from_secs(2)), exp.next());
-        assert_eq!(Some(Duration::from_secs(2)), exp.next());
-        assert_eq!(None, exp.next());
+        assert_eq!(Some(Duration::from_secs(2)), it.next());
+        assert_eq!(Some(Duration::from_secs(2)), it.next());
+        assert_eq!(Some(Duration::from_secs(2)), it.next());
+        assert_eq!(None, it.next());
     }
 
     #[test]
     fn test_constant_with_times() {
-        let mut exp = ConstantBuilder::default().with_max_times(1).build();
+        let mut it = ConstantBuilder::default().with_max_times(1).build();
 
-        assert_eq!(Some(Duration::from_secs(1)), exp.next());
-        assert_eq!(None, exp.next());
+        assert_eq!(Some(Duration::from_secs(1)), it.next());
+        assert_eq!(None, it.next());
     }
 
     #[test]
@@ -175,4 +185,13 @@ mod tests {
         fastrand::seed(7);
         assert!(dur > Duration::from_secs(1));
     }
+
+    #[test]
+    fn test_constant_without_max_times() {
+        let mut it = ConstantBuilder::default().without_max_times().build();
+
+        for _ in 0..10_000 {
+            assert_eq!(Some(Duration::from_secs(1)), it.next());
+        }
+    }
 }
diff --git a/backon/src/backoff/exponential.rs b/backon/src/backoff/exponential.rs
index cee9932..44729b8 100644
--- a/backon/src/backoff/exponential.rs
+++ b/backon/src/backoff/exponential.rs
@@ -91,6 +91,16 @@ impl ExponentialBuilder {
         self
     }
 
+    /// Set no maximum delay for the backoff.
+    ///
+    /// The delay will keep increasing.
+    ///
+    /// _The delay will saturate at `Duration::MAX` which is an **unrealistic** delay._
+    pub fn without_max_delay(mut self) -> Self {
+        self.max_delay = None;
+        self
+    }
+
     /// Set the maximum number of attempts for the current backoff.
     ///
     /// The backoff will stop if the maximum number of attempts is reached.
@@ -98,6 +108,16 @@ impl ExponentialBuilder {
         self.max_times = Some(max_times);
         self
     }
+
+    /// Set no maximum number of attempts for the current backoff.
+    ///
+    /// The backoff will not stop by itself.
+    ///
+    /// _The backoff could stop reaching `usize::MAX` attempts but this is **unrealistic**._
+    pub fn without_max_times(mut self) -> Self {
+        self.max_times = None;
+        self
+    }
 }
 
 impl BackoffBuilder for ExponentialBuilder {
@@ -246,6 +266,21 @@ mod tests {
         assert_eq!(None, exp.next());
     }
 
+    #[test]
+    fn test_exponential_no_max_times_with_default() {
+        let mut exp = ExponentialBuilder::default()
+            .with_min_delay(Duration::from_secs(1))
+            .with_factor(1_f32)
+            .without_max_times()
+            .build();
+
+        // to fully test we would need to call this `usize::MAX`
+        // which seems unreasonable for a test as it would take too long...
+        for _ in 0..10_000 {
+            assert_eq!(Some(Duration::from_secs(1)), exp.next());
+        }
+    }
+
     #[test]
     fn test_exponential_max_delay_with_default() {
         let mut exp = ExponentialBuilder::default()
@@ -258,6 +293,22 @@ mod tests {
         assert_eq!(None, exp.next());
     }
 
+    #[test]
+    fn test_exponential_no_max_delay_with_default() {
+        let mut exp = ExponentialBuilder::default()
+            .with_min_delay(Duration::from_secs(1))
+            .with_factor(10_000_000_000_f32)
+            .without_max_delay()
+            .with_max_times(4)
+            .build();
+
+        assert_eq!(Some(Duration::from_secs(1)), exp.next());
+        assert_eq!(Some(Duration::from_secs(10_000_000_000)), exp.next());
+        assert_eq!(Some(Duration::MAX), exp.next());
+        assert_eq!(Some(Duration::MAX), exp.next());
+        assert_eq!(None, exp.next());
+    }
+
     #[test]
     fn test_exponential_max_delay_without_default_1() {
         let mut exp = ExponentialBuilder {
diff --git a/backon/src/backoff/fibonacci.rs b/backon/src/backoff/fibonacci.rs
index 49ec073..feae5d2 100644
--- a/backon/src/backoff/fibonacci.rs
+++ b/backon/src/backoff/fibonacci.rs
@@ -75,6 +75,16 @@ impl FibonacciBuilder {
         self
     }
 
+    /// Set no maximum delay for the backoff.
+    ///
+    /// The delay will keep increasing.
+    ///
+    /// _The delay will saturate at `Duration::MAX` which is an **unrealistic** delay._
+    pub fn without_max_delay(mut self) -> Self {
+        self.max_delay = None;
+        self
+    }
+
     /// Set the maximum number of attempts for the current backoff.
     ///
     /// The backoff will stop if the maximum number of attempts is reached.
@@ -82,6 +92,16 @@ impl FibonacciBuilder {
         self.max_times = Some(max_times);
         self
     }
+
+    /// Set no maximum number of attempts for the current backoff.
+    ///
+    /// The backoff will not stop by itself.
+    ///
+    /// _The backoff could stop reaching `usize::MAX` attempts but this is **unrealistic**._
+    pub fn without_max_times(mut self) -> Self {
+        self.max_times = None;
+        self
+    }
 }
 
 impl BackoffBuilder for FibonacciBuilder {
@@ -153,7 +173,7 @@ impl Iterator for FibonacciBackoff {
                 // If current delay larger than max delay, we should stop increment anymore.
                 if next < self.max_delay.unwrap_or(Duration::MAX) {
                     if let Some(prev) = self.previous_delay {
-                        next += prev;
+                        next = next.saturating_add(prev);
                         self.current_delay = Some(next);
                     }
                     self.previous_delay = Some(cur);
@@ -235,6 +255,27 @@ mod tests {
         assert_eq!(None, fib.next());
     }
 
+    #[test]
+    fn test_fibonacci_no_max_delay() {
+        let mut fib = FibonacciBuilder::default()
+            .with_max_times(4)
+            .with_min_delay(Duration::from_secs(10_000_000_000_000_000_000))
+            .without_max_delay()
+            .build();
+
+        assert_eq!(
+            Some(Duration::from_secs(10_000_000_000_000_000_000)),
+            fib.next()
+        );
+        assert_eq!(
+            Some(Duration::from_secs(10_000_000_000_000_000_000)),
+            fib.next()
+        );
+        assert_eq!(Some(Duration::MAX), fib.next());
+        assert_eq!(Some(Duration::MAX), fib.next());
+        assert_eq!(None, fib.next());
+    }
+
     #[test]
     fn test_fibonacci_max_times() {
         let mut fib = FibonacciBuilder::default().with_max_times(6).build();
@@ -247,4 +288,18 @@ mod tests {
         assert_eq!(Some(Duration::from_secs(8)), fib.next());
         assert_eq!(None, fib.next());
     }
+
+    #[test]
+    fn test_fibonacci_no_max_times() {
+        let mut fib = FibonacciBuilder::default()
+            .with_min_delay(Duration::from_secs(0))
+            .without_max_times()
+            .build();
+
+        // to fully test we would need to call this `usize::MAX`
+        // which seems unreasonable for a test as it would take too long...
+        for _ in 0..10_000 {
+            assert_eq!(Some(Duration::from_secs(0)), fib.next());
+        }
+    }
 }