Under certain assumptions we show that a wavelet frame {(Aj, bj,k)ψ}j,k∈Z:={|det Aj|−1/2ψ(Aj−1j(x−bj,k))}j,k∈Z in L2(Rd) remains a frame when the dilation matrices Aj and the translation parameters bj, k are perturbed. As a special case of our result, we obtain that if {T(Aj, AjBn)ψ}j∈Z, n∈Zd is a frame for an expansive matrix A and an invertible matrix B, then {T(A'j, AjBλn) }j∈Z,n∈Zd is a frame if kA−jA’j−I‖2≤εand‖λn− n‖∞≤n for sufficiently smallε, n>0.