  We discuss a simple phenomenological Landau theory of phase transitions with
two coupled single-component order parameters and compare the results with
available experimental data. The model corresponds to the case of a ferroic
system, in which ferromagnetic and ferroelectric transitions originally occur
at temperatures $T_M$ and $T_f$, respectively. For $T_f>T_M$ the
magnetoelectric coupling strongly renormalizes the magnetic transition
temperature, $T_M\to T_{RM}$ (with $T_{RM}>>T_M$), as well as generates an
additional anomaly in ferroelectric subsystem $T_{RM}$. Full susceptibility
tensor has also been determined. The concept of \textit{Arrot plot} is replaced
by the \textit{Arrot planes} which appear when both types of order coexist. The
results are in good overall agreement with experimental data for the
ferroelectromagnetic BiMnO$_3$. We also estimate the contribution of Gaussian
fluctuations of both order parameters, that lead to corrections to the
mean-field specific heat. Those corrections are still insufficient even though
other quantities agree quite well with experiment. We calculate the temperature
dependence of the coherence length for both types of order as well.
