Many biochemical reactions require a close spatial contact of two distant DNA sites (for example, initiation of transcription and site-specific recombination). Such a contact, or collision, is a random event caused by thermal fluctuations of the DNA conformation. However, one single contact is, in general, not sufficient for the chemical transformation: the act of reaction is preceded by many "unsuccessful" collisions. If the probability of a "success" is very small, the reaction is slow and its rate is determined by the local concentration of one DNA site around the other. On the other hand, a large "success" probability corresponds to a fast reaction limited by the time of the first collision. These two extreme cases have been studied earlier by Monte Carlo and Brownian dynamics simulations. In the present study the emphasis is made on reactions of intermediate rate. The Brownian dynamics technique can be applied here as well, although "simulated" collisions by no means coincide with the "real" ones. Peculiarities of supercoiled DNA lead to some unusual features of intrachain reactions. In particular, for relatively slow reactions, the role of the three-dimensional structure of the molecule becomes unimportant and the kinetics are determined by the quasi-one-dimensional reptation of the strands forming the superhelix.