  We derive superalgebras in many types of supersymmetric M-brane backgrounds.
The backgrounds examined here include the cases of the M-wave and the
M-Kaluza-Klein monopole. On the basis of the obtained algebras, we deduce all
the supersymmetric non-orthogonal intersections of the M-Kaluza-Klein monopole
and the M-5-brane at angles. In addition, we present a 1/4 supersymmetric
worldvolume 3-brane soliton on the M-5-brane in the M-5-brane background as an
extended solution of the 3-brane solitons of the M-5-brane by Howe, Lambert and
West. This soliton can be interpreted as a certain intersection of three
M-5-branes.
