Electron transfer in a bath with slow and fast degrees of freedom is described by a theory based on a microscopic spin-boson Hamiltonian, where the spectral function has two different relaxation times. Evolution dynamics is rigorously found, under the assumption that omega(c)(s)/Gamma root E-rs/kT much less than 1. Here omega(c)(s) is the cutoff frequencies in the spectral function for the slow modes, E-rs is the reorganization energy of slow degrees of freedom, and Gamma(-1) is the reaction time. This is a short-time approximation for slow modes and a long-time approximation for the reaction. It is found that the time-dependent probability is presented as the averaged probability with a random Gaussian reaction heat with the mean value epsilon-E-rs, where epsilon is the original reaction heat. The partial dynamics (when the random heat is fixed) is determined by the parameters of the fast degrees of freedom. The time-dependent probability is a nonexponential function. At later times, P(t)similar to t(-Erf/Ers) for activationless reactions (here E-rf is the reorganization energy of the fast degrees of freedom). Experimental dependence of P(t) in a log-log scale reveals the ratio E-rf/E-rs. The reaction is shown to be almost insensitive to temperature. It is pointed out that the nonexponential dependence of the time-dependent probability can be fitted by two exponential functions, and, consequently, be incorrectly interpreted as a two step process. The theory can explain the main features (nonexponentiality and temperature insensitivity) of primary electron transfer in photosynthetic bacteria.