In this paper with the notion of weighted sharing of values we study the uniqueness of nonlinear differential polynomials of meromorphic
functions sharing a nonzero polynomial and obtain two results which improves and generalizes the results due to L. Liu [Uniqueness of meromorphic functions and differential polynomials, Comput.
Math. Appl., 56 (2008), 3236-3245.] and P. Sahoo [Uniqueness and weighted value sharing of meromorphic functions, Applied. Math. E-Notes., 11 (2011), 23-32.].