A simple model is used to study a tunable amplitude-modulated mode-loc
ked Co:MgF2 laser, The dynamics in the case of detuning of the round-t
rip frequency from resonance with the frequency of modulation is inves
tigated and a rich family of behaviours is found. The dependences of t
he solutions on the pump rate, the modulation depth and the presence o
f a filtering element are explored. Observed phenomena are clarified i
n terms of the pulse evolution inside the cavity which appears to play
a considerable role in the dynamics.