A short exact sequence 0\(\to A\to B\to C\to 0\) of (right unitary) R- modules is said to be copure if every cofinitely related R-module is injective with respect to this sequence. The first part of the paper studies some properties of copure exact sequences. In the second part the relations between copure and pure (in the sense of P. M. Cohn) exact sequences are investigated. Among other results, the coincidence of the classes of copure and pure exact sequences over a commutative semilocal co-noetherian ring (or almost Dedekind domain) is stated.