In this paper, the use of optimal Karhunen-Loeve (KL) transform for quantization of speech line spectrum frequency (LSF) coefficients is studied. Both scalar quantizer (SQ) and vector quantizer (VQ) schemes are developed to encode efficiently the transform parameters after operating one or two-dimensional KL transform. Furthermore, the SQ schemes are also combined with entropy coding by using Huffman variable length coding (VLC). The basic idea in developing these schemes is utilizing the strong correlation of LSF parameters to reduce the bit rate for a given level of fidelity. Since the use of global statistics for generating the coding scheme may not be appropriate, we propose several adaptive KL transform systems (AKL) to encode the LSF parameters. The performance of all systems for different bit rates is investigated and adequate comparisons are made. It is shown that the proposed KL transform coding systems introduce as good as or better performance for both SQ and VQ in the examined bit rates compared to other methods in the field of LSF coding.