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Motivated by Lazer-Leach type results, we study the existence of periodicsolutions for systems of functional-differential equations at resonance with anarbitrary even-dimensional kernel and linear deviating terms involving ageneral delay of the form $\int_0^{2\pi}u(t+s)\,d\lambda(s)$, where $\lambda$is a finite regular signed measure. Our main technique shall be the CoincidenceDegree Theorem due to Mawhin.

Systems of functional-differential equations periodic solutions for systems of functional-differential semilinear equations at resonance