  We study the supersymmetric Gelfand-Dickey algebras associated with the
superpseudodifferential operators of positive as well as negative leading
order. We show that, upon the usual constraint, these algebras contain the N=2
super Virasoro algebra as a subalgebra as long as the leading order is odd. The
decompositions of the coefficient functions into N=1 primary fields are then
obtained by covariantizing the superpseudodifferential operators. We discuss
the problem of identifying N=2 supermultiplets and work out a couple of
supermultiplets by explicit computations.
