We consider the following system of Lyness-type difference equations: x 1 (n + 1) = (a k x k (n) + b k)/x k−1 (n − 1), x 2 (n + 1) = (a 1 x 1 (n) + b 1)/x k (n − 1), x i (n + 1) = (a i−1 x i−1 (n) + b i−1)/x i−2 (n − 1), i = 3,4,...,k, where a i , b i , i = 1,2,...,k, are positive constants, k ≥ 3 is an integer, and the initial values are positive real numbers. We study the existence of invariants, the boundedness, the persistence, and the periodicity of the positive solutions of this system.

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