  Stick-slip, manifest as intermittent tangential motion between two solids, is
a well-known friction instability that occurs in a number of natural and
engineering systems. In the context of adhesive polymer interfaces, this
phenomenon has often been solely associated with Schallamach waves, which are
termed slow waves due to their low propagation speeds. We study the dynamics of
a model polymer interface using coupled force measurements and high speed
\emph{in situ} imaging, to explore the occurrence of stick-slip linked to other
slow wave phenomena. Two new waves---slip pulse and separation pulse---both
distinct from Schallamach waves, are described. The slip pulse is a sharp
stress front that propagates in the same direction as the Schallamach wave,
while the separation pulse involves local interface detachment and travels in
the opposite direction. Transitions between these stick-slip modes are easily
effected by changing the sliding velocity or normal load. The properties of
these three waves, and their relation to stick-slip is elucidated. We also
demonstrate the important role of adhesion in effecting wave propagation.
