  In this paper we show that the componentwise maxima ofweakly dependent
bivariate stationary Gaussian triangular arrays converge in distribution after
normalisation to H\"usler-Reiss distribution. Under a strong dependence
assumption, we prove that the limit distribution of the maxima is a mixture of
a bivariate Gaussian distribution and H\"usler-Reiss distribution. Another
finding of our paper is that the componentwise maxima and componentwise minima
remain asymptotically independent even in the settings of H\"usler and Reiss
(1989) allowing further for weak dependence. Further we derive an almost sure
limit theorem under the Berman condition for the components of the triangular
array.
