  We present a semiclassical calculation, based on classical action
correlations implemented by means of a matrix integral, of all moments of the
Wigner--Smith time delay matrix, $Q$, in the context of quantum scattering
through systems with chaotic dynamics. Our results are valid for broken time
reversal symmetry and depend only on the classical dwell time and the number of
open channels, $M$, which is arbitrary. Agreement with corresponding random
matrix theory reduces to an identity involving some combinatorial concepts,
which can be proved in special cases.
