EN
The Blume-Emery-Griffiths model for spins S=1 in a bilayer with z=5 nearest neighbours is studied with the use of Gaussian fluctuations approximation. The fluctuations of two molecular fields, connected with two order parameters, are introduced. Their influence on phase diagrams for non-negative values of the biquadratic coupling constant is taken under consideration. The results are compared with those obtained by the mean-field approximation and discussed.