Adaptive differential pulse code modulation (ADPCM) with forward gain-adaptive quantizer and second-order switched predictor based on correlation is presented in this article. Predictor consists of a bank of predetermined predictors for each block of speech samples, avoiding the need to solve, or quantize predictor coefficients during the coding process. The adaptation consists of switching to one of this predictors based on the values of the first and second order correlation coefficients. The theoretical model is generalization of the DPCM with the first order switched predictor for an arbitrary prediction order. Experimental results for ADPCM with the second-order four/eight state switched prediction based on correlation are provided.