We analyzed bifurcations of periodic regimes generated in the systems of two identical relaxation oscillators under strong coupling through a ‘‘slow’’ ~inhibitory! variable. It was numerically shown that complex spatiotemporal behavior is observed near the boundaries of stability of the known antiphase periodic attractor and inhomogeneous steady states. Specifically, the following attractors were found: ~i! a set of cycles of the antiphase type, each of which consists of one full-amplitude excursion and of the different number of smallamplitude high-frequency oscillations ~the period of antiphase mixed-mode regimes is much greater than that of simple antiphase oscillations!, ~ii! inhomogeneous regimes of the above described type ~out-of-phase mixed mode! with unequal numbers of small oscillations for different oscillators, ~iii! period doubling cascades of the out-of-phase mixed mode that lead to the appearance of chaotic attractors. We showed that the modes found are not specific for our particular model; however, they are common for several classes of models and sensitive to the stiffness of oscillators. We discuss also conditions for the generation of such regimes. @S1063651X~96!06806-7#