  We have analyzed the ${\bar B}^0\to \pi^0\pi^0$ puzzle in three kinds of
models beyond the standard model (SM). It is shown that the minimal flavor
violation (MFV) models, the minimal supersymmetric standard model (MSSM), and
the two Higgs doublet models (2HDM) I and II can not give an explanation of the
${\bar B}^0\to \pi^0\pi^0$ puzzle within $1 \sigma$ experimental bounds and the
model III 2HDM can explain the puzzle without a conflict with other
experimental measurements. If the constraint on $C_{8g}$ from $b\to s g$ is not
imposed, for all kinds of insertions considered there are regions of parameter
space, where the scalar quark mass is larger (much larger) than the gluino mass
in the case of LR or RL (LL or RR), in which the puzzle can be resolved within
$1 \sigma$ experimental bounds.
