Changes in gene expression play a fundamental role in phenotypic evolution. Transcriptome evolutionary dynamics have so far mainly been compared among distantly related species and remain largely unexplored during rapid organismal diversification, in which gene regulatory changes have been suggested as particularly effective drivers of phenotypic divergence. Here, we studied gene expression evolution in a model system of adaptive radiation, the cichlid fishes of African Lake Tanganyika. By comparing gene expression profiles of six different organs in 74 cichlid species representing all subclades of this radiation, we demonstrate that the rate of gene expression evolution varies among organs, transcriptome parts, and the subclades of the radiation, indicating different strengths of selection. We found that the non-coding part of the transcriptome evolved more rapidly than the coding part, and that the gonadal transcriptomes evolved more rapidly than the somatic ones, with the exception of liver. We further show that the rate of gene-expression change was not constant over the course of the radiation but accelerated at its later phase. Finally, we show that – at the per-gene level – the evolution of expression patterns is dominated by stabilizing selection.