This paper deals with relative
satellites and derived functors of functors from an additive category A into an
Abelian category. The satellites and derived functors are defined by universal
properties relative to classes S of morphisms of A that contain all morphisms whose
domain is an initial object of A, that are closed under multiplication and
basecoextension, and whose elements have cokernels. The existence of satellites and
derived functors relative to S is shown by a method due to D. Buchsbaum without
using the existence of either enough S-injective or S-projective objerts in
A. With the proper notion of S-exactness in A the exactness of the long
satellite resp. derived functor sequence is established under quite general
assumptions.
