Two-state Brownian motion is considered. One state is subjected to white noise while the other one is exposed to dichotomous noise. Such motion is described by a set of three connected Fokker-Planck equations. The switch probability density functions between the states are assumed to have a single exponential form. The equations for the partial moments of the particle velocity are solved recursively. The first moment vanishes as t→ while the second moment defines the effective diffusion coefficient. Estimates have been made of the Brownian motion near the critical point.