  The Einstein-Maxwell theory has black hole solutions with electric and
magnetic charges. In the standard model for particle physics, dyons with
electric and magnetic charges would have been formed in the early universe. We
derive the equations of motion of black hole binaries with electric and
magnetic charges and explore some features of static orbits. We calculate the
total emission rates of energy and angular momentum due to gravitational and
electromagnetic radiations from dyonic binary black holes in different cases.
It is shown that the emission rates of energy and angular momentum due to
gravitational and electromagnetic radiations have the same dependence on the
conic angle for different orbits. Moreover, we obtain the evolutions of orbits
and find that a circular orbit remains circular while an elliptic orbit becomes
quasi-circular due to electromagnetic and gravitational radiations. Our results
provide rich information about black hole binaries with electric and magnetic
charges and can be used to test black holes with magnetic charges.
