The evolution of RNA viruses under antiviral pressure is characterized by high mutation rates and strong selective forces that induce extremely rapid changes of protein sequences. This makes the course of molecular evolution directly observable on time scales of months. Here we study the interplay between selection for drug resistance and selection for thermodynamic stability in the protease (PR) and the reverse transcriptase (RT) of human immunodeficiency virus type 1 (HIV-1) clones extracted from two patients with complex treatment histories. This analysis shows that folding thermodynamic properties may fluctuate very strongly in the course of quasispecies evolution under selective pressure. For the first case, our data suggest that folding efficiency of the RT is sacrificed at the advantage of drug resistance, while the corresponding PR seems to undergo selection for thermodynamic stability in the absence of substitutions associated to resistance. The PR of the second case is not submitted to antiviral pressure during the period analyzed and seems to initiate random fluctuations that lead to the accidental increase of its folding efficiency. In summary, joint consideration of sequence evolution and thermodynamic parameters can represent a more comprehensive approach for the study of the evolution of RNA viruses.