A new microscopic approach to the problem of cooperative spin crossover in molecular crystals containing binuclear complexes as structural units has been developed. The cooperative interaction arising from the coupling of the molecular mode to the acoustic phonons represents the cornerstone of the approach. Another important ingredient of the model is the Coulomb interaction between the spin crossover ions in the binuclear cluster that is different in the ls-ls, hs-ls, and hs-hs states (ls, low spin; hs, high spin). The suggested approach makes it possible to reproduce all types of transitions observed in binuclear compounds including two-step transitions. The applicability of the developed approach is illustrated by the interpretation of the experimental data on spin transitions for the binuclear [{Fe(bpym)(NCSe)₂}₂bpym] and [{Fe(bt)(NCS)₂}₂bpym] cluster compounds.