Summary: ``The aim of paper is to find the condition under which a Fréchet-valued function $f\in C^\infty(\{0\})$ admitting meromorphic extension along some pencil of complex lines can be meromorphically extended to a neighborhood of $0\in\Bbb C^N$. Some auxiliary results concerning the domains of existence for Fréchet-valued meromorphic functions, Rothstein's theorem, Levi extension theorem for meromorphic functions with values in a locally complete space, convergence of formal power series of Fréchet-valued homogeneous polynomials are also proved in this work.''