  We present a method, based on commutator methods, for the spectral analysis
of uniquely ergodic dynamical systems. When applicable, it leads to the
absolute continuity of the spectrum of the corresponding unitary operators. As
an illustration, we consider time changes of horocycle flows, skew products
over translations and Furstenberg transformations. For time changes of
horocycle flows, we obtain absolute continuity under assumptions weaker than
the ones to be found in the literature.
