The paper discusses a versatile family of Monte Carlo methods for the sequential optimization of stochastic systems. The method selects a sequence of successive one-dimensional search directions, defines a (stochastic) search in each of the directions, where the data used for both the one-dimensional search and the direction determination are merely noise-corrupted observations on the system. The method is more general than stochastic approximation, it converges to a stationary point even in the presence of multiple minima, and it uses rather natural logics. A convergence theorem is proved.