An iterative block training method for support vector classifiers (SVCs) based on weighted least squares (WLS) optimization is presented. The algorithm, which minimizes structural risk in the primal space, is applicable to both linear and nonlinear machines. In some nonlinear cases, it is necessary to previously find a projection of data onto an intermediate-dimensional space by means of either principal component analysis or clustering techniques. The proposed approach yields very compact machines, the complexity reduction with respect to the SVC solution is especially notable in problems with highly overlapped classes. Furthermore, the formulation in terms of WLS minimization makes the development of adaptive SVCs straightforward, opening up new fields of application for this type of model, mainly online processing of large amounts of (static/stationary) data, as well as online update in nonstationary scenarios (adaptive solutions). The performance of this new type of algorithm is analyzed by means of several simulations.