Various aspects of the Nahm equations in three and seven dimensions are inv
estigated. The residues of the variables at simple poles in the seven-dimen
sional case form an algebra. A large class of matrix representations of thi
s algebra is constructed. The large N limit of these equations is taken by
replacing the commutators by Moyal brackets, and a set of nontrivial soluti
ons in a generalized form of Wigner distribution functions is obtained. (C)
1999 American Institute of Physics. [S0022-2488(99)03706-8].