The Fibonacci cube Γ n is the subgraph of hypercube Q n induced by the binary strings that contain no two consecutive 1s, and the Lucas cube Λ n is obtained from Γ n by removing vertices that start and end with 1. For p ≥ 1 , the subgraph of hypercube Q n induced by the strings that contain no 1 0 s 1 for all s < p is called the Fibonacci p -cube and denoted by Γ n p , and the subgraph of hypercube Q n induced by the strings in which 1 0 s 1 ( s < p ) is forbidden in a circular manner is called the Lucas p -cube and denoted by Λ n p . Clearly, the Fibonacci cube Γ n is Γ n 1 , and the Lucas cube Λ n is Λ n 1 . In this paper, first of all, some general properties of Γ n p and Λ n p , such as the recursive structures, the number of vertices and edges, the diameter, the radius and centers, and the medianicity, are investigated. Furthermore, based on these properties, the Wiener index and cube polynomials of Γ n p and Λ n p are studied. Finally, some problems and questions are proposed.