In this paper the author introduces a definition of continuability with respect to a part of the variables, for the solutions of systems of ordinary differential equations, which slighty changes the analogous concept introduced by C. Corduneanu in the theory of partial stability, and moreover gives sufficient conditions for this ”partial” continuability. This allows one to formulate criteria for the global existence and the partial boundedness of the solutions of ordinary differential equations, by using the comparison method together with Lyapunov functions, generalizing known results of R. Conti and T. Yoshizawa.