We present the implementation of the radiative corrections of the Higgs
sector in three public computer codes for the evaluation of the particle
spectrum in the Minimal Supersymmetric Standard Model, Softsusy, Spheno and
SuSpect. We incorporate the full one-loop corrections to the Higgs boson masses
and the electroweak symmetry breaking conditions, as well as the two-loop
corrections controlled by the strong gauge coupling and the Yukawa couplings of
the third generation fermions. We include also the corrections controlled by
the tau Yukawa coupling that we derived for completeness. The computation is
consistently performed in the DRbar renormalisation scheme. In a selected
number of MSSM scenarios, we study the effect of these corrections and analyse
the impact of some higher order effects. By considering the renormalisation
scheme and scale dependence, and the effect of the approximation of zero
external momentum in the two-loop corrections, we estimate the theoretical
uncertainty on the lighter Higgs boson mass to be 3 to 5 GeV. The uncertainty
on Mh due to the experimental error in the measurement of the SM input
parameters is approximately of the same size. Finally, we discuss the
phenomenological consequences, using the latest value of the top quark mass. We
find, in particular, that the most conservative upper bound on the lighter
Higgs boson mass in the general MSSM is Mh < 152 GeV and that there is no lower
bound on the parameter tan(beta) from non-observation of the MSSM Higgs bosons
at LEP2