We present intersecting p-brane solutions of eleven-dimensional superg
ravity (M-branes) which upon toroidal compactification reduce to non-e
xtreme rotating black holes, We identify harmonic functions, associate
d with each M-brane, and non-extremality functions, specifying a devia
tion from the BPS limit. These functions are modified due to the angul
ar momentum parameters, which specify the rotation along the transvers
e directions of the M-branes. We spell out the intersection rules for
the eleven-dimensional space-time metric for intersecting (up to three
) rotating M-brane configurations (and a boost along the common inters
ecting direction). (C) 1997 Elsevier Science B.V.