An equivalent stochastic feedback system can be found for many recursive identification and adaptive control schemes. This equivalent feedback system has a certain structure which is used here for constructing near supermartingales, allowing the establishment of a.s. convergence. Explicit convergence conditions are then obtained for recursive identification and adaptive control schemes which admit an equivalent stochastic feedback representation of the form considered. The usefulness of the results is illustrated by their application to the straightforward convergence analysis of several schemes which have not been considered previously, and to the re-derivation of the known convergence conditions for two other schemes.