A theory of identification is developed for a general stochastic model whose probability law is determined by a finite number of parameters. It is shown under weak regularity conditions that local identifiability of the unknown parameter vector is equivalent to nonsingularity of the information matrix. The use of "reduced-form" parameters to establish identifiability is also analyzed. The general results are applied to the familiar problem of determining whether the coefficients of a system of linear simultaneous equations are identifiable.