A vectorial generalization of the ADPCM system is introduced. Once the speech signal is grouped in vectors, they are coded using a vector predictor (VP) and a vector quantizer (VQ). Both subsystems are continously adaptive; the VQ is matched the signal power; two algorithms (VLMS and VGAL) are considered to adapt the predictor. At the bit stream corresponding to 2 bits per signal sample, the coding system rends a segmented signal to noise ratio equivalent to other existing coders.