Linear relations, containing measurement errors in input and output data, are taken into account in this paper. Parameters of these so-called \emph{errors-in-variables} (EIV) models can be estimated by minimizing the \emph{total least squares} (TLS) of the input-output disturbances. Such an estimate is highly non-linear. Moreover in some realistic situations, the errors cannot be considered as independent by nature. \emph{Weakly dependent} (α- and φ-mixing) disturbances, which are not necessarily stationary nor identically distributed, are considered in the EIV model. Asymptotic normality of the TLS estimate is proved under some reasonable stochastic assumptions on the errors. Derived asymptotic properties provide necessary basis for the validity of block-bootstrap procedures.