  The difficulties for non-standard solar models (NSSM) in resolving the solar
neutrino problem are discussed stressing the incompatibility of the
gallium--Kamiokande data, and of the gallium--chlorine data. We conclude that
NSSM's cannot explain simultaneously the results of any two of the solar
neutrino data (chlorine, Kamiokande and gallium). We address further the
question whether the MSW solution exists for NSSM's (e.g. models with $^8$B
neutrino flux much lower than the standard one and/or central temperature $T_c$
very different from $T_c^{\text{SSM}}$). We demonstrate that the MSW solution
exists and is very stable relative to changes of $S_{17}$ ($S$-factor for $p$ +
$^7$Be reaction) and $T_c$. In particular, $\Delta m^2$ is almost constant
while $\sin^2 2\theta$ depends on the exact values of $S_{17}$ (or
$^8$B-neutrino flux) and $T_c$.
