Abstract.In this paper, we shall consider the case where a stationary vector process {Xt} belongs to one of two categories described by two hypothesesπ1andπ2. These hypotheses specify that {Xt} has spectral density matricesf(Λ) andg(Λ) underπ1andπ2, respectively. Although Gaussianity of {Xt} is not assumed, we can formally make the Gaussian likelihood ratio (GLR) based onX(1),…X(T). Then an approximationI(f:g) of the GLR is given in terms off(Λ) andg(Λ). Iff(Λ) andg(Λ) are known, we can useI(f:g) as a classification statistic. It is shown thatI(f:g) is a consistent classification criterion in the sense that the misclassification probabilities converge to zero asT→∝. Whengis contiguous tof, we discuss non‐Gaussian robustness ofI(f:g). A sufficient condition for the non‐Gaussian robustness will be given. Also a numerical ex