We compute the O(alpha (l)alpha (s)) two-loop corrections to the neutral Hi
ggs boson masses in the Minimal Supersymmetric extension of the Standard Mo
del. An appropriate use of the effective potential allows us to obtain simp
le analytical formulae, valid for arbitrary values of m(A) and of the mass
parameters in the stop sector. We elucidate some subtleties of the effectiv
e potential calculation, and find full agreement with the numerical output
of the existing diagrammatic calculation. We discuss in detail the limit of
heavy gluino. (C) 2001 Elsevier Science B.V. All rights reserved.