In this paper, we present a new generalization to compute determinants and inverses of r−circulant matricesQn = circr (( b a ) ξ(2) 2 q1, ( b a ) ξ(3) 2 q2, . . . , ( b a ) ξ(n+1) 2 qn ) andLn = circr (( b a ) ξ(1) 2 l1, ( b a ) ξ(2) 2 l2, . . . , ( b a ) ξ(n) 2 ln ) whose entries are the biperiodic Fibonacci and the biperiodic Lucas numbers, respectively. Also, we express determinants of the matrices Qn and Ln by using only the biperiodic Fibonacci and the biperiodic Lucas numbers