  In this paper, we prove two normality criteria for a family of meromorphic
functions. The first criterion extends a result of Fang and Zalcman[Normal
families and shared values of meromorphic functions II, Comput. Methods Funct.
Theory, 1(2001), 289 - 299] to a bigger class of differential polynomials
whereas the second one leads to some counterexamples to the converse of the
Bloch's principle.
