Origin of new biological functions is a complex phenomenon ranging from single-nucleotide substitutions to the gain of new genes via horizontal gene transfer or duplication. Neofunctionalization and subfunctionalization of proteins is often attributed to the emergence of paralogs that are subject to relaxed purifying selection or positive selection and thus evolve at accelerated rates. Such phenomena potentially could be detected as anomalies in the phylogenies of the respective gene families. We developed a computational pipeline to search for such anomalies in 1,834 orthologous clusters of archaeal genes, focusing on lineage-specific subfamilies that significantly deviate from the expected rate of evolution. Multiple potential cases of neofunctionalization and subfunctionalization were identified, including some ancient, house-keeping gene families, such as ribosomal protein S10, general transcription factor TFIIB and chaperone Hsp20. As expected, many cases of apparent acceleration of evolution are associated with lineage-specific gene duplication. On other occasions, long branches in phylogenetic trees correspond to horizontal gene transfer across long evolutionary distances. Significant deceleration of evolution is less common than acceleration, and the underlying causes are not well understood; functional shifts accompanied by increased constraints could be involved. Many gene families appear to be "highly evolvable," that is, include both long and short branches. Even in the absence of precise functional predictions, this approach allows one to select targets for experimentation in search of new biology.