  We demonstrate numerically the existence of nonlinear Tamm oscillations at
the interface between a substrate and one-dimensional waveguide array with both
cubic and saturable, self-focusing and self-defocusing nonlinearity. Light is
trapped in the vicinity of the boundary of the array due to the interplay
between the repulsive edge potential and Bragg reflection inside the array. In
the special case when this potential is linear these oscillations reduce
themselves to surface Bloch oscillations.
