Consider an overdetermined system \(AX=B\), where \(A\in\mathbb{R}^{m\times n}\), \(B\in\mathbb{R}^{m\times d}\). Any \(X\in\mathbb{R}^{n\times d}\) is called a total least squares solution of this system, provided \(X\) solves \(\widehat A X=\widehat B\), where \([\widehat A,\widehat B]\in\mathbb{R}^{m\times(n+d)}\) minimizes \(\| [A,B]-[\widehat A,\widehat B]\|_ F\) subject to \(R(\widehat B)\subseteq R(\widehat A)\). If \(A\) is (nearly) rank-deficient,this total least squares problem becomes highly ill-conditioned or even unsolvable. To oversome these problems, an extension of the total least squares problem, the so-called nongeneric total least squares problem, is described, where additional constraints on the solution space are imposed. This method is compared with other approaches in linear regression.