  We show that a nonlinear, piecewise-smooth, planar dynamical system can
exhibit canard phenomena. Canard solutions and explosion in nonlinear,
piecewise-smooth systems can be qualitatively more similar to the phenomena in
smooth systems than piecewise-linear systems, since the nonlinearity allows for
canards to transition from small cycles to canards ``with heads." The canards
are born of a bifurcation that occurs as the slow-nullcline coincides with the
splitting manifold. However, there are conditions under which this bifurcation
leads to a phenomenon called super-explosion, the instantaneous transition from
a globally attracting periodic orbit to relaxations oscillations. Also, we
demonstrate that the bifurcation---whether leading to canards or
super-explosion---can be subcritical.
