  We explore commutativity up to a factor, $AB=\lambda BA$, for bounded
operators in a complex Hilbert space. Conditions on the possible values of the
factor $\lambda$ are formulated and shown to depend on spectral properties of
the operators involved. Commutativity up to a unitary factor is considered for
pairs of self-adjoint operators. Examples of nontrivial realizations of such
commutation relations are given.
