We studied the Jx-Jy Blume–Capel model in an external field with Jx=−Jy using the Bethe Approximation of the Cluster Variation Method. At zero field the phase diagram is equivalent to the phase diagram of the classical Blume–Capel model with ferromagnetic interactions, in which the ferromagnetic phase is replaced by a superantiferromagnetic one. When a magnetic field is applied, we observe a mixed phase intermediate between the superantiferromagnetic and the paramagnetic phases. Depending on the values of the single-spin anisotropy parameter we find first and second order phase transitions and tricritical points.