  We present a simple and self-contained approach to establish the unique
continuation property for some classical evolution equations of second order in
a cylindrical domain. We namely discuss this property for wave, parabolic and
Sch\"odinger operators with time-independent principal part. Our method is
builds on two-parameter Carleman inequalities combined with unique continuation
across a pseudo-convex hypersurface with respect to the space variable. The
most results we demonstrate in this work are more or less classical. Some of
them are not stated exactly as in their original form.
