In this paper we study the convergence properties of the Crandall-Liggett sequence <img border=0 width=226 height=23 src="http://fbpe/img/cubo/v13n2/art02-01.jpg" alt="Descripción: Descripción: http://fbpe/img/cubo/v13n2/art02-01.jpg">, for A a nonlinear operator on some important non-locally convex F-spaces (called p-Fréchet spaces with 0 < p < 1) and the generation of the corresponding strongly continuous one-parameter nonlinear semigroups.