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We present a layered predictive compression approach for time-consistent dynamic 3D meshes. The algorithm decomposes each frame of a dynamic 3D mesh in layers employing patch-based mesh simplification techniques. This layered decomposition is consistent in time. Following the predictive coding paradigm, local temporal and spatial dependencies between layers and frames are exploited for compression. Prediction is performed vertex-wise from coarse to fine layers exploiting local linear and non-linear dependencies between vertex locations for compression. It is shown that a non-linear predictive exploitation of the proposed layered configuration of vertices can improve the compression performance upon other state-of-the-art approaches by more than 15% in domains relevant for applications.