Angular variations of the g-factors and linewidth value were recorded at X-band, at room temperature, and at 77 K. The temperature dependence of the g-factors was measured along the principal g-tensor axes in the temperature range from 4.2 K to 300 K. The rigid lattice g-factors at 4.2 K are: g. = 2.428, gy = 2.138, and gx = 2.058. The gx value very slowly increases linearly on heating, whereas gz and gy nonlinearly tend towards their average value. This is a typical behaviour of Cu(II) EPR in Tutton salt crystals, however the g(T) dependence is much less pronounced in (NH4)2Cu(BeF4)2 •6H20 as compared to the Cu(II) doped salts. The results are described in terms of the two vibronic coupling models of the strong Jahn-Teller effect. It is shown that the models are not adequate to describe the vibronic g-factor behaviour in paramagnetic Cu(II) crystals which is attributed to the cooperative Jahn-Teller effect existing in these crystals.