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The authors introduce and investigate two new subclasses $\mathcal{M}^{*}(\alpha)$ and $N^{*}(\alpha)$ of normalized analytic functions satisfying certain coefficient inequalities in the open unit disk U. The main results of the present paper provide various interesting properties of functions belonging to the classes $\mathcal{M}^{*}(a)$ and $N^{*}(\alpha)$ . Some of these properties include (for example) several coefficient inequalities, distortion bounds and inclusion relationships for the function classes which are considered here.

Some coefficient inequalities and distortion bounds associated with certain new subclasses of analytic functions