  A new type of Coulomb gas is defined, consisting of arbitrary numbers of
point charges of two species executing Brownian motions under the influence of
their mutual electrostatic repulsion. Being a generalization of a model of
identical particles introduced by Dyson as a dynamical system describing
non-equilibrium state of various random matrix ensembles, our system gives an
exact mathematical description of the Brownian motion of charges of magnitudes
$ Q_1 $ and $ Q_2 $, such that $ \beta Q_1 Q_2 = 1 $ on the line or circle,
where $\beta$ is an inverse temperature of the gas.
