  For m>n\geq 0 and 1\leq d\leq m, it is shown that the q-Euler number
E_{2m}(q) is congruent to q^{m-n}E_{2n}(q) mod (1+q^d) if and only if m\equiv n
mod d. The q-Sali\'e number S_{2n}(q) is shown to be divisible by
(1+q^{2r+1})^{\left\lfloor \frac{n}{2r+1}\right\rfloor} for any r\geq 0.
Furthermore, similar congruences for the generalized q-Euler numbers are also
obtained, and some conjectures are formulated.
