A novel type of triple-stranded DNA structure was proposed by several groups to play a crucial role in homologous recognition between single- and double-stranded DNA molecules. In this still putative structure a duplex DNA was proposed to co-ordinate a homologous single strand in its major groove side. In contrast to the well-characterized pyrimidine-purine-pyrimidine triplexes in which the two like strands are antiparallel and which are restricted to poly-pyrimidine-containing stretches, the homology-specific triplexes would have like strands in parallel orientation and would not be restricted to any particular sequence provided that there is a homology between interacting DNA molecules. For many years the stereo-chemical possibility of forming homology-dependent three- or four-stranded DNA structures during the pairing stage of recombination reactions was seriously considered in published papers. However, only recently has there been a marked increase in the number of papers that have directly tested the formation of triple-stranded DNA structures during the actual pairing stage of the recombination reaction. Unfortunately the results of these tests are not totally clear cut; while some laboratories presented experimental evidence consistent with the formation of triplexes, others studying the same or very similar systems offered alternative explanations. The aim of this review is to present the current state of the central question in the mechanism of homologous recombination, namely, what kind of DNA structure is responsible for DNA homologous recognition. Is it a novel triplex structure or just a classical duplex?