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The paper presents a geometric method of finding periodic solutions of retarded functional differential equations (RFDE) $x^{\text{'}}\left(t\right)=f(t,x_t)$, where f is T-periodic in t. We construct a pair of subsets of ℝ × ℝⁿ called a T-periodic block and compute its Lefschetz number. If it is nonzero, then there exists a T-periodic solution.