The dynamical behavior of two mutually coupled semiconductor lasers is studied experimentally, numerically, and analytically for weak coupling. The lasers have dissimilar relaxation oscillation frequencies and intensities, and their mutual coupling strength may be asymmetric. We find experimentally that the lasers preferentially entrain to the relaxation oscillation frequency of either one of the lasers. But quasiperiodic synchronization, where both relaxation oscillation frequencies appear, is possible. We show that there 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 transition can be observed experimentally if the injection strength is continuously increased from zero.