In strong magnetic fields up to 20 T quasistatic measurements of the magnet
ic-field-induced electric polarization have been performed in LiNiPO4 singl
e crystals between 4.2 and similar to 25 K. The magnetoelectric (ME) effect
has been studied in detail near the Neel temperature. The temperature hyst
eresis of the polarization induced by a magnetic field was found. An anomal
ous temperature dependence of the magnetoelectric susceptibility during the
phase transition and the ME "butterfly loop" were observed. The phenomenol
ogical 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 invari
ant in the free energy expansion which is linear in the spatial derivatives
. Hence the phase transition to a space-modulated spin structure is possibl
e. The influence of such a structure on the linear magnetoelectric effect i
s examined.