  The Fibonacci sequence has been generalized in many ways. One of them is
defined by the relation $t_n=at_{n-1}+t_{n-2}$ if $n$ is even,
$t_n=bt_{n-1}+t_{n-2}$ if $n$ is odd, with initial values $t_0=0$ and $t_1=1$,
where $a$ and $b$ are positive integers. This sequence is called biperiodic
Fibonacci sequence. In this paper, we introduce a $q$-analogue of this
sequence. We prove several identities of $q$-analogues of the Fibonacci
sequence. We give algebraic and combinatorial proofs.
