  A thorough analysis of the evolutions of bipartite systems characterized by
the \lq effective absence\rq\, of interaction between the two subsystems is
reported. First, the connection between the concepts underlying
Interaction-Free Evolutions (IFE) and Decoherence-Free Subspaces (DFS) is
explored, showing intricate relations between these concepts. Second, starting
from this analysis and inspired by a generalization of DFS already known in the
literature, we introduce the notion of generalized IFE (GIFE), also providing a
useful characterization that allows to develop a general scheme for finding
GIFE states.
