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 Periodic solutions for a type of neutral system with variable parameters Keywords:Periodic solution; Coincidence degree; Neutral system Abstract: In this paper, we firstly analyze some properties of the linear difference operator $$[Ax](t)=x(t)-C(t)x(t-\tau),$$ where $C(t)$ is a $n\times n$ matrix function, and then using Mawhin's continuation theorem, a first-order neutral functional differential system is studied. Some new results on the existence and stability of periodic solutions are obtained. The results are related to the deviating arguments $\tau$ and $\mu$. Meanwhile, the approaches to estimate a $prior$ bounds of periodic solutions are different from the corresponding ones of the known literature.