Characteristics of observed bursts of single channel openings were derived recently for two particular ion channel mechanisms. In this paper these methods are generalized so that the observable characteristics of bursts can be calculated directly for any mechanism that has transition probabilities that are independent of time as long as the process is at equilibrium or is maintained in a steady state by an energy supply. General expressions are given for the distributions of the open time, the number of openings per burst, the total open time per burst, the gaps within and between bursts, and so on. With the aid of these general results a single computer program can be written that will provide numerical values for such distributions for any postulated mechanism, given only the transition rates between the various states. The results are illustrated by a numerical example of a mechanism in which two agonist molecules can bind sequentially, and either singly or doubly occupied receptor ion channels may open. The analogous theory is also given for the case where bursts of channel openings are grouped into clusters; many of the results bear a close analogy with those found for simple bursts.