This thesis is concerned with a wide class of truncated stochastic approximation (SA) procedures. These procedures have three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function. Convergence, rate of convergence, and asymptotic linearity of the SA procedures are established in a very general setting. Main results are supplemented with corollaries to establish different sets of sufficient conditions, with the main emphases on the parametric statistical estimation. The theory is illustrated by examples and special cases. Properties of these procedures are illustrated and discussed using a simulation study.