Purine nucleoside phosphorylase (PNP) is a ubiquitous enzyme of the nucleoside salvage pathway and it is characterized by non-Michaelis kinetics. Kinetic data in many cases (for some substrates or some concentration range of a co-substrate) are best described by the double hyperbolic equation. It was suggested that this is an indication of this enzyme being an example of a morpheein, i.e. the protein that exists as an equilibrium of the quaternary structure isoforms. In this paper we summarize our already published data for calf spleen and E. coli PNPs, as well as some new experiments conducted for the latter enzyme, which show the influence of various parameters on the activity and oligomeric structure in the solution of both proteins. We have been using a variety of methods including enzyme kinetics, steady-state emission spectroscopy, and size exclusion chromatography, as well as analytical ultracentrifugation and circular dichroism spectroscopy. Taken together the results let us conclude that calf spleen and E. coli PNPs are not morpheeins and in solution under a variety of conditions they exist, respectively, as a stable trimer and hexamer (a trimer of dimers).