In order to provide a unified treatment for the continuum and digital realm of multivariate data, Guo, Labate, Weiss and Wilson [Electron. Res. Announc. Amer. Math. Soc. 10 (2004), 78-87] introduced the notion of AB-wavelets in the context of multiscale analysis. We continue and extend their work by studying the frame properties of AB-wavelet systems { DADBTkψ` (k ∈ Zn; 1 5 ` 5 L) } in L2(Rn). More precisely, we establish four theorems giving sufficient conditions under which the AB-wavelet system constitutes a frame for L2(Rn). The proposed conditions are stated in terms of the Fourier transforms of the generating functions,