\textit{A. Kapteyn} and \textit{T. J. Wansbeek} [ibid. 51, 1847-1849 (1983; Zbl 0542.62056)] considered the following multiple linear regression model with errors in variables: \[ (1)\quad y_ j=\xi '\!_ j\beta +\epsilon_ j,\quad (2)\quad x_ j=\xi_ j+\nu_ j,\quad j=1,...,n, \] where \(\xi_ j\), \(x_ j\), \(\nu_ j\), and \(\beta\) are k-vectors, \(y_ j\), \(\epsilon_ j\) are scalars. The \(\xi_ j\) are unobservable variables: instead the \(x_ j\) are observed. The measurement errors \(\nu_ j\) are unobservable as well and it is assumed that \(\nu_ j\sim N(0,\Omega)\) and \(\epsilon_ j\sim N(0,\sigma^ 2)\) for all j. The \(\nu_ j\) and \(\epsilon_ j\) are mutually independent and independent of \(\xi_ j\). The \(\xi_ j\) are considered as random drawings from some, as yet unspecified, multivariate distribution with zero mean. For the case \(k=1\) \textit{O. Reiersøl} [ibid. 18, 375-389 (1950; Zbl 0040.225)] has shown that normality of \(\xi_ j\) is the only distributional assumption which spoils identification. For the case \(k\geq 1\) and the components of \(\xi_ j\) are mutually independent, \textit{Y. Willassen} [Scand. J. Stat., Theory Appl. 6, 89-91 (1979; Zbl 0427.62088)] has shown that none of the components of \(\xi_ j\) should be normally distributed to guarantee identifiability of \(\beta\). Kapteyn and Wansbeek did not assume independency of the components of \(\xi_ j\) and they stated the following proposition: the parameter vector \(\beta\) is identified if and only if there does not exist a linear combination of \(\xi_ j\) which is normally distributed. The necessity part in this proposition is incorrect, i.e. it may well be that a normally distributed linear combination of \(\xi_ j\) does not spoil the identifiability of \(\beta\). Here I present necessary and sufficient conditions for identification of \(\beta\).