This paper studies the algebraic properties and perturbation theory of the generalized total least squares problem (GTLS) AX≈B, in which is free of error, and the error contained in is of the form EC with C a given nonsingular matrix. The problem was proposed by Van Huffel and Vandewalle. The solvability conditions, formulas for the GTLS solutions, their residuals, and the minimum norm correction matrices are obtained, and a perturbation theory for the GTLS problem is given.