When a signal passing through a delay line (e.g., an echo device) is regenerated and fed back to the input in such a way that it emerges at a higher volume each time it passes through the line. Eventually, the signal amplitude exceeds what the line is capable of handling, and then the signal becomes progressively more distorted each time through.
This occurs particularly with analog delay lines such as tape of BBD-based devices. Because these types of delay lines attentuate the signal passing through, it is necessary to regenerate the signal with some gain if a large number of echoes or repeats is desired. However, there can be a fine line between the amount of gain that results in the desired number of repeats, and the amount of gain that causes runaway. A few delay devices have anti-runaway circuits. But on most, once runaway begins, it will continue indefinitely until the performer intervenes. Analog delay lines in runaway, if the delay time is long enough, will produce a distinctive effect: the input signal gradually morphs into a machine-like noise, with substantial amounts of apparent reverb. Sometimes performers provoke this, and then try to keep the line at unity gain, to achieve the evolving effect.
On the other hand, runaway at very short delay times usually produces unpleasant howling or screeching noises. Digital delays vary greatly as to how they react to runaway. However, most digital delays are designed so that provoking runaway is difficult; since the delay line itself has no attentuation, it is easy to design the regeneration circuit so that the end-to-end gain never rises above unity.