We present results of a numerical study of static, spherically symmetric so
lutions of a Julia-Zee dyon coupled to a massless dilaton. We have found th
at coupling a dilaton to the dyon sets an upper limit on its electric charg
e. A reason for this is given based on the finite energy boundary condition
s imposed on the solutions. Finally, we also show the existence of excited
states indexed by the number of zeros of the gauge field. [S0556-2821(99)04
102-8].