A concept of a proper projective semimodule is introduced and proper projective resolutions are used to construct derived functors of additive functors from the category of cancellative semimodules to the category of cancellative semimodules. We investigate exactness of the long sequence of derived functors associated to a proper short exact sequence of semimodules. Also, the right derived functors of the functor Hom are described as proper extensions of semimodules.