  In this paper we classify the irreducible quasifinite highest weight modules
over the orthogonal and symplectic types Lie subalgebras of the Lie algebra of
the matrix quantum pseudo differential operators. We also realize them in terms
of the irreducible quasifinite highest weight modules of the Lie algebras of
infinite matrices with finitely many nonzero diagonals and its classical Lie
subalgebras of types B, C and D.
