In strong magnetic fields up to 20 T quasistatic measurements of the magnetic-field-induced electric polarization have been performed in LiNiPO4 single crystals between 4.2 and ∼25 K. The magnetoelectric (ME) effect has been studied in detail near the Neel temperature. The temperature hysteresis of the polarization induced by a magnetic field was found. An anomalous temperature dependence of the magnetoelectric susceptibility during the phase transition and the ME "butterfly loop" were observed. The phenomenological theory of the magnetoelectric effect in LiCoPO4 and LiNiPO4 has been developed. A tentative explanation of the existence of the magnetoelectric "butterfly loop" is given. It is shown that there is a non-Lifshitz invariant in the free energy expansion which is linear in the spatial derivatives. Hence the phase transition to a space-modulated spin structure is possible. The influence of such a structure on the linear magnetoelectric effect is examined.