The mechanism responsible for the explosion of solid mixtures of nitrogen tetroxide (N2O4) and hydrazine (HZ) or methyl-substituted HZs, detected experimentally by slow warming from 77 to 203-223 K, has been elucidated by quantum chemical calculations using the Vienna ab initio simulation package code. The result of the calculation for the reaction of a N2O4 molecule embedded in the middle of the N2H4 molecular crystal, N2O4@HZ23, indicates that a loose nonconventional transition state (TS) occurring by stretching the O2N-NO2 bond up to 2.18 Å with the concerted rotation of one of the NO2 groups producing the reactive ONONO2 isomer (ONONO2@HZ23) has a low 13.1 kcal/mol barrier at TS1; the process is exothermic by 45 kcal/mol, reflecting the much stronger ONONO2 binding with N2H4. A further simultaneous reaction of ONONO2 with 2N2H4 in the same unit cell occurs with a small 1.4 kcal/mol barrier producing NO3 - + NH2N(H)NO + N2H5 + with an overall exothermicity of 70.2 kcal/mol. The mechanism for this last-step reaction is distinctly different from that in the gas phase taking place via a five-centered concert mechanism giving N2H3NO and HNO3, which can further produce N2H5 +NO3 - by the rapid acid-base neutralization process. On the basis of the predicted structure, energy, and vibrational frequencies at TS1, we estimated the rate constant at 218 K for the N2O4-ONONO2 isomerization reaction in solid N2H4 to be 1.35 s-1, giving the half-life of N2O4@HZ23 to be as short as 0.5 s. This result can explain why the slow warming of the solid mixtures of N2O4 and N2H4 from 77 K exploded reproducibly at 218 K.