The Blume-Emery-Griffiths model Hamiltonian with the transverse crystal field interaction (Delta), the transverse (Omega) and longitudinal (h) external magnetic fields in addition to the usual exchange interactions both bilinear (J) and biquadratic (K) and the crystal-field interaction (D) is studied via the scheme of mean-field approximation. Thermal variation of the longitudinal and transverse dipolar (S) and quadrupolar (Q) order parameters of the model is investigated extensively for the various values of the interaction parameters. Besides the stable solutions, metastable and unstable solutions of the order parameters are also found. In the absence of the longitudinal external magnetic field, the phase transitions are examined and the phase diagrams are obtained for several values of the coupling strengths and the system parameters in the five different planes. A comparison with other approximate techniques is also made. (C) 1999 Elsevier Science B.V. All rights reserved.