[en] We extend Siegel's generalised Virasoro algebra for Type I superstring to Type IIA superstrings. Since the Type IIA superstring can be obtained from the eleven-dimensional supermembrane by dimensional reduction, it is natural to seek a Type IIA Virasoro algebra that can be derived from one for the supermembrane. This leads to an algebra containing an infinite number of generators, including as a subset those of the direct sum of a left-moving and a right-moving Type I algebra. We also find a remarkable property of the Kac-Moody algebra for supermembranes and Type IIA superstrings which is likely to play an important role in finding the superspace constraints for d=11, N=1 and d=10, N=2α supergravity theories, by a generalisation of the notion of integrability along light-like lines. (author). 9 refs