  Classical homological algebra takes place in additive categories. In homotopy
theory such additive categories arise as homotopy categories of ``additive
groupoid enriched categories'', in which a secondary analog of homological
algebra can be performed. We introduce secondary chain complexes and secondary
resolutions leading to the concept of secondary derived functors. As a main
result we show that the E_3-term of the Adams spectral sequence can be
expressed as a secondary derived functor. This result can be used to compute
the E_3-term explicitly by an algorithm.
