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In this paper, with the help of measure of noncompactness together with Darbo-type fixed point theorem, we focus on the infinite system of third-order differential equations u???i + au??i + bu?i + cui = fi(t, u1(t), u2(t),...) where fi ? C(R x R?,R) is ?-periodic with respect to the first coordinate and a,b,c ? R are constants. The aim of this paper is to obtain the results with respect to the existence of ?-periodic solutions of the aforementioned system in the Banach sequence space lp (1 ? pdoi:10.2298/fil2011861p fatcat:4fzalz47jnfe7kw3c73xuba4z4