Given an R-module V, the near-ring of homogeneous maps MR(V) is the set of maps {f:V→ V |f(rv)=rf(v)for allrb.epsis;Rand v b.epsis;V} endowed with point-wise addition and composition of functions as multiplication. Modules with the property thatMR(V)= EndR(V)and those with the property thatMR(V)is a ring, will be characterized in certain cases. It will also be investigated whether these are local properties.