A description is given of the high Reynolds number (R [Gt ] 1) laminar fluid motion in the neighbourhood of the trailing edge of a flat plate undergoing small amplitude sinusoidal oscillations in a uniform supersonic stream. It is shown that for oscillations of frequency ω* = O(R¼) and amplitude h* = O(R−½) a rational description of the flow at the trailing edge is based on a ‘triple-deck’ structure, which is a familiar feature of steady trailing-edge flows. The theory may be extended in a straightforward manner to include slow oscillations of the plate, and it is shown in general that the occurrence of separation at the trailing edge is dependent upon the magnitude of the product of the frequency and amplitude of oscillation, and that if ω* [les ] O(R½) then the flow is maintained right up to the trailing edge provided that h*ω* [Lt ] R−¼. The precise condition for the occurrence of separation is found for frequencies in the range ω* R−¼.