In the present investigation, we consider two new subclasses $\Cal N_\Sigma^\mu(\alpha,\lambda)$ and $\Cal N_\Sigma^\mu(\beta,\lambda)$ of bi-univalent functions defined in the open unit disk $\Cal U=\{z:|z|<1\}$. Besides, we find upper bounds for the second and third coefficients for functions in these new subclasses.