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By means of the Krasnoselskii fixed piont theorem, periodic solutions are found for a neutral type delay differential system of the form $$x^{\text{'}}\left(t\right)+c{x}^{\text{'}}\left(t-\tau \right)=A\left(t,x\left(t\right)\right)x\left(t\right)+f\left(t,x\left(t-r_1\left(t\right)\right),\cdots ,x\left(t-r_k\left(t\right)\right)\right).$$