A theory is developed to describe a recent infrared pump-probe experiment in water. This theory is a statistical theory, similar to those elaborated earlier to interpret ultraviolet and visible spectra. Nonlinear optical processes involved are analyzed in terms of four-time correlation functions of the electric dipole moment of the system and of the incident electric fields, respectively. An analytical expression for the transient infrared signal is presented. The observed spectral characteristics are attributed to a gradual thermalization of the initial, pump-prepared state. The substructure of the observed bands is interpreted. This experiment probes the kinetics of conversion of H-bonds of different lengths into each other.