Abstract The experiments described in this paper were designed to elucidate the mechanism of elongation of a polynucleotide chain catalysed by polynucleotide phosphorylase. The problem has been approached in three different ways, essentially: (1) examination of the size distribution of the end products isolated during the course of the reaction; (2) search for the intermediates, in particular for primary products freed from the enzyme before the termination of the elongation process; (3) study of the enzyme-substrate complexes. The results show that: (a) the polymers formed are of high molecular weight and homogeneous in size; (b) no polynucleotide chains with intermediate chain length are found; (c) among the polymerization products found free from the enzyme one cannot detect any significant amounts of small oligonucleotides. These results suggest that the elongation process catalysed by the enzyme involves a mechanism of non-dissociation of the growing polynucleotide, which can be visualized as the reverse of phosphorolysis. This work also presents data on the formation of enzyme-polynucleotide complexes, the conditions under which they are formed and isolated, together with some of their properties. The results illustrate a high stability for such complexes and suggest that there might be more than one site of fixation, i.e. in addition to the active site on which the 3′OH end should be attached: somehow the polynucleotide molecule covers part of the enzyme surface with multiple sites of fixation. Consequently, a model based on a “rolling on” mechanism which would involve a one-by-one addition of each unit, the non-dissociation of the intermediates and the fixation of the growing polymer rolling on the enzyme, is proposed for the elongation process catalysed by polynucleotide phosphorylase. In addition, new methods, such as a dialysis technique for the synthesis of polymers, a filtration technique as well as “simultaneous nuclease attack” for the search of free intermediates, are introduced.