We present a theoretical study of the interaction of tight DNA crossovers with eukaryotic type II DNA topoisomerases. A quantitative analysis of the role of the enzyme during anaphase first shows that a tight DNA crossover should be an intermediate of the strand-passage reaction. We then focus on the initial steps of the strand-passage reaction in vitro which lead to the formation of a ternary complex ES1S2 between the enzyme and a tight DNA crossover (where E is the enzyme, S1 (respectively S2) is the first (respectively the second) DNA segment bound by the enzyme, and S1S2 is a tight crossover). This formation can be described by three equilibrium association constants: KS1 (for the reaction E+S1left arrow over right arrow ES1), KS2 (for ES1+S2left arrow over right arrow ES1S2), and KS (for E+S1S2left arrow over right arrow ES1S2) Using published experimental data obtained on the Drosophila enzyme, we derive rough estimates for the intrinsic equilibrium constants KS1 ( approximately 2.5x10(6) M-1) and KS2 ( approximately 10(4) M-1) and for Ks. The huge value found for Ks, about 5x10(16) M-1, suggests that the ternary complex bears a close resemblance with a transition state complex, and is consistent with the notion of a capture of the crossover by a protein clamp. We give a theoretical description of analogues of tight DNA crossovers which consist of two DNA segments stabilized by a covalent crosslinking. Such analogues are predicted to bind the enzyme with a high affinity and should be useful tools for the study of the enzyme.