  Transverse mode coupling instability of a single bunch caused by oscillating
wake field is considered in the paper. The instability threshold is found at
different frequencies of the wake with space charge tune shift taken into
account. The wake phase advance in the bunch length from 0 up to $4\pi$ is
investigated. It is shown that the space charge can push the instability
threshold up or down dependent on the phase advance. Transition region is
investigated thoroughly, and simple asymptotic formulas for the threshold are
represented.
