  We list the spectrum generating algebras for string theory and M-theory
compactified on various backgrounds of the form $AdS_{d+1} \times S^n$. We
identify the representations of these algebras which make up the classical
supergravity spectra and argue for the presence of these spectrum generating
algebras in the classical string/M-theory. We also discuss the role of the
spectrum generating algebras on the conformal field theory side.
