Detailed investigations of magnetization, ferromagnetic resonance, magnetostriction and torque measurements on pure EuSe single crystals revealed that anomalous behaviours concerning the unusual phase diagram can be explained by the magnon softening due to near cancellation of exchange interactions, J1 + J2 ≈ 0, and by the thus enhanced effects of J3 and the biquadratic interaction j1. These parameters were determined unambiguously. Anomalous behaviour of the anisotropy energy in the ferromagnetic state is also explained consistently. Molecular field calculations of K1 and K2 due to dipole interaction are shown not to be adequate because of the neglect of magnon dispersion. For the first time, we found from the spin wave analysis the different natures of K1 and K2 between magnetic and pseudo-dipole interactions.