The dominant view in protein science is that a three-dimensional (3-D) structure is a prerequisite for protein function. In contrast to this dominant view, there are many counterexample proteins that fail to fold into a 3-D structure, or that have local regions that fail to fold, and yet carry out function. Protein without fixed 3-D structure is called intrinsically disordered. Motivated by anecdotal accounts of higher rates of sequence evolution in disordered protein than in ordered protein we are exploring the molecular evolution of disordered proteins. To test whether disordered protein evolves more rapidly than ordered protein, pairwise genetic distances were compared between the ordered and the disordered regions of 26 protein families having at least one member with a structurally characterized region of disorder of 30 or more consecutive residues. For five families, there were no significant differences in pairwise genetic distances between ordered and disordered sequences. The disordered region evolved significantly more rapidly than the ordered region for 19 of the 26 families. The functions of these disordered regions are diverse, including binding sites for protein, DNA, or RNA and also including flexible linkers. The functions of some of these regions are unknown. The disordered regions evolved significantly more slowly than the ordered regions for the two remaining families. The functions of these more slowly evolving disordered regions include sites for DNA binding. More work is needed to understand the underlying causes of the variability in the evolutionary rates of intrinsically ordered and disordered protein.