We study numerically the dynamics of spiral waves in an excitable medium wi
th negative restitution. For our study we use two models of the excitable m
edium: a cellular automaton and a reaction-diffusion model. There are no si
gnificant effects of negative restitution as long as the slope of the resti
tution curve is less steep than -1. In media with slopes steeper than -1, t
he dynamics of spiral waves can change significantly: (1) the average resti
tution time jumps to a value where the slope of the restitution curve is ab
out -1; (2) spiral waves can break up into turbulent patterns. We discuss a
possible connection between such instabilities and fibrillation in atrial
tissue.