Report discussing the problem of point-to-point radio communication on the moon. Equations and curves are presented to estimate power requirements in lunar communication systems. Consideration is given to ground wave attenuation over both layered and non-layered grounds, antenna ground losses in situations where ground screens are impractical, noise level estimates in the receiving system, and the effects on propagation of possible lunar ionospheres. An example of the calculation of required power for a particular communication system is given, and further studies are suggested.