This paper considers the problem of criteria for the identifiability of a structural equation which is one of a set of equations linear in the parameters but not in the variables. The criteria are developed in terms of parameter restrictions of the rank condition type. By expansion in Taylor's series and combination with the results of Fisher [2], these results can be easily extended to far more general nonlinear systems. THE USUAL treatment of identifiability criteria is one of linear structures and homogeneous linear restrictions on the coefficients of a single structural equation.2 Recently, I generalized this to the case where restrictions on such coefficients merely have continuous first derivatives; however, it was still the case that only linear structural equations were considered.3 While Anderson and Rubin showed how to obtain limited information, maximum likelihood estimates for the parameters of a linear equation which is part of a nonlinear system and have shown that such estimates have the usual consistency properties,4 they assumed that the equation in question was identifiable under coefficient restrictions of the usual type and did not consider the prior question of the application of the rank and order conditions for identifiability to nonlinear systems.5 This paper considers that question explicitly for a restricted (but highly important) class of nonlinear systems, namely, for systems linear in the unknown coefficients and in the residuals, but not necessarily linear in the variables. Extension to far more general nonlinear cases can be readily accomplished by expansion in Taylor series in the parameters and combina

Edited by L.H. Klaassen, L.M. Koyck and H.J. Witteveen, Presented on the occasion of his 25 years jubilee as a professor at the Netherlands School of Economics at Rotterdam. (With a bibliography of professor Tinbergen's work).