  We analyze the relationship of generalized conditional symmetries of
evolution equations to the formal compatibility and passivity of systems of
differential equations as well as to systems of vector fields in involution.
Earlier results on the connection between generalized conditional invariance
and generalized reduction of evolution equations are revisited. This leads to a
no-go theorem on determining equations for operators of generalized conditional
symmetry. It is also shown that up to certain equivalences there exists a
one-to-one correspondence between generalized conditional symmetries of an
evolution equation and parametric families of its solutions.
