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We study the conformal properties of the multi-constraint KP hierarchy andits nonstandard partner by covariantizing their corresponding Lax operators.The associated second Hamiltonian structures turn out to be nonlocal extensionof $W_n$ algebra by some integer or half-integer spin fields depending on theorder of the Lax operators. In particular, we show that the complicated secondHamiltonian structure of the nonstandard multi-constraint KP hierarchy can besimplified by factorizing its Lax operator to multiplication form. We thendiagonalize this simplified Poisson matrix and obtain the free-fieldrealizations of its associated nonlocal algebras.Comment: 14 pages, RevTex, no figures, typos correcte

NONLOCAL EXTENDED CONFORMAL ALGEBRAS ASSOCIATED WITH MULTICONSTRAINT KP HIERARCHY AND THEIR FREE FIELD REALIZATIONS