  We examine the conformal property of the second Hamiltonian structure of
constrained KP hierarchy derived by Oevel and Strampp. We find that it
naturallygives a family of nonlocal extended conformal algebras. We give two
examples of such algebras and find that they are similar to Bilal's V algebra.
By taking a gauge transformation one can map the constrained KP hierarchy to
Kuperschmidt's nonstandard Lax hierarchy. We consider the second Hamiltonian
structure in this representation. We show that after mapping the Lax operator
to a pure differential operator the second structure becomes the sum of the
second and the third Gelfand-Dickey brackets defined by this differential
operator. We show that this Hamiltonian structure defines the W-U(1)-Kac-Moody
algebra by working out its conformally covariant form.
