Since a quasi-Banach space of sequences named quasi-Sobolev space is not locally convex it is not possible to speak about integrability of each continuous function. The main aim of this work is to get conditions sufficient for existence of Riemann integral for the function with values in such space. We use the properties of metrizability and local pseudoconvexivity of the space to show the existence of integral for an analytic function. Besides the introduction and bibliography, the article

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... udes two sections. In the first section the mentioned properties of quasi-Banach spaces are discussed. In the second section we obtain the conditions for integration of function with values in quasi-Banach spaces of sequences.