The dynamical behavior of two mutually coupled semiconductor lasers is stud
ied experimentally, numerically, and analytically for weak coupling. The la
sers have dissimilar relaxation oscillation frequencies and intensities, an
d their mutual coupling strength may be asymmetric. We find experimentally
that the lasers preferentially entrain to the relaxation oscillation freque
ncy of either one of the lasers. But quasiperiodic synchronization, where b
oth relaxation oscillation frequencies appear, is possible. We show that th
ere exist two distinct mechanisms leading to these regimes corresponding to
either a bifurcation to a mixed-mode solution or a bifurcation induced by
the delay of the mutually injected signal. However, only the second transit
ion can be observed experimentally if the injection strength is continuousl
y increased from zero. [S1050-2947(99)00705-2].