We discuss the notion of Liapunov exponent for integrate-and-fire (IF) type dynamical
systems. In contrast to smooth flows there is a contribution to the IF Liapunov
exponent arising from the discontinuous nature of the firing mechanism. Introducing
the notion of an IF mode-locked state we are able to show that linear stability
is consistent with the requirement of a negative IF Liapunov exponent. We apply
our results to IF systems that may be used to study the entrainment of biological
This is a pre-print. The definitive version: COOMBES, S., 1999. Liapunov exponents and mode-locked solutions for integrate-and-fire dynamical systems. Physics Letters A, 255(1-2), pp.49-57, is available at: http://www.sciencedirect.com/science/journal/03759601.