UDC 517.968 Uniqueness of Solutions for One Class of Linear Equations of the First Kind with Two Variables Z. A. Kadenova Ministry of Education and Science of the Kyrgyz Republic 257, K. Tynystanova str., Bishkek, 720044, Kyrgyzstan This article is devoted to the study of the uniqueness of solutions of linear integral equations of the first kind with two independent variables in which the operator generated by the kernel, is not compact operator. <...> The relevance of the problem is due to the needs in development of new approaches for the regularization and uniqueness of the solution of linear integral equations of the first kind with two independent variables. <...> For approximate solutions of such tasks, stable to small variations of the initial data, we use the solutions derived by the method of regularization and belonging to the class of incorrectly formulated tasks. <...> More specifically, fundamental results for Fredholm integral equations of the first kind were obtained in [6], where regularizing operators in the sense of M.M.Lavrent’ev vere constructed for solutions of linear Fredholm integral equations of the first kind. <...> For linear Volterra integral equations of the first and third kinds with smooth kernels, the existence of a multiparameter family of solutions was proved in [7]. <...> The regularization and uniqueness of solutions to systems of nonlinear Volterra integral equations of the first kind were investigated in [4,5]. <...> Asanov A. Regularization, Uniqueness and Existence of Solutions of Volterra Equations of the First Kind. — Utrecht: VSP, 1998. 1. <...> Imanaliev M. I., Asanov A. On Solutions of Systems of Nonlinear Two Dimensional Volterra Integral Equations of the First Kind // Doklady Akademii Nauk.— 1991. — Vol. 317, No 2. — Pp. 330–333. 6. <...> Shishatskii S. P., Asanov A., Atamanov E. R. Uniqueness Problems for Degenerating Equations and Nonclassical Problems. — Utrecht: VSP, 2001. <...> УДК 517.968 Единственность решений для одного класса интегральных уравнений первого рода с двумя независимыми переменными З. <...> This article is devoted to the study of the uniqueness of solutions of linear integral equations of the first kind with two independent variables in which the operator generated by the kernel, is not compact operator. <...> The relevance of the problem is due to the needs in development of new approaches for the regularization and uniqueness of the solution of linear integral equations of the first kind <...>