In the present investigation, the author introduces two interesting subclasses of normalized meromorphic univalent functions $w=f(z)$ defined on $ ilde{Delta}:={z{in}mathbb{C}:1<{mid}z{mid}<{infty}}$ whose inverse $f^{-1}(w)$ is also univalent meromorphic in $ ilde{Delta}$. Estimates for the initial coefficients are obtained for the functions in these new subclasses.