  We derive the equations of motion of dyonic black hole binaries with electric
and magnetic charges and explore features of static orbits. By using a
Newtonian method with the inclusion of radiation reaction, we calculate the
total emission rate of energy and angular momentum due to gravitational
radiation and electromagnetic radiation for circular orbits. Moreover, we
obtain the evolutions of orbits and calculate merger times of dyonic binaries.
We show that electric and magnetic charges significantly suppress the merger
times of dyonic binaries. Our results provide rich information about dyonic
binaries and can be used to test black holes with magnetic charges.
