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The fixed point theorem of Krasnoselskii and the concept of large contractions are employed to show the existence of a periodic solution of a nonlinear integro-differential equation with variable delay $$x^{\text{'}}\left(t\right)=-{\int }_{t-\tau \left(t\right)}^{t}a(t,s)g\left(x\left(s\right)\right)ds+\frac{d}{dt}Q(t,x(t-\tau \left(t\right)))+G(t,x\left(t\right),x(t-\tau \left(t\right))).$$ We transform this equation and then invert it to obtain a sum of two mappings one of which is completely continuous and the other is a large contraction. We choose suitable conditions for $\tau$, $g$, $a$, $Q$ and $G$ to show that this sum of mappings fits into the framework of a modification of Krasnoselskii’s...