Abstract: A novel predictive lossless coding scheme is proposed. The prediction is based on a new weighted cascaded least mean squared (WCLMS) method. To obtain both a high compression ratio and a very low encoding and decoding delay, the residuals from the prediction are encoded using either a variant of adaptive Huffman coding or a version of adaptive arithmetic coding. WCLMS is especially designed for music/speech signals. It can be used either in combination with psycho-acoustically prefiltered signals (an idea presented in [1]) to obtain perceptually lossless coding, or as a stand-alone lossless coder. Experiments on a database of moderate size and a variety of pre-filtered mono-signals show that the proposed lossless coder (which needs about 2 bit/sample for pre-filtered signals) outperforms competing lossless coders, such as ppmz, bzip2, Shorten, and LPA C, in terms of compression ratios. The combination of WCLMS with either of the adaptive coding schemes is also shown to achieve better compression ratios and lower delay than an earlier scheme combining WCLMS with Huffman coding over blocks of 4,096 samples.