  We analyze the octet baryon masses and the pion/kaon--nucleon $\sigma$--terms
in the framework of heavy baryon chiral perturbation theory. We include {\it
all} terms up-to-and-including quadratic order in the light quark masses,
$m_q$. We develop a consistent scheme to estimate low--energy constants related
to scalar--isoscalar operators in the framework of resonance exchange involving
one--loop graphs. The pertinent low--energy constants can only be estimated up
to some finite coefficients. Including contributions from loop graphs with
intermediate spin--3/2 decuplet and spin--1/2 octet states and from tree graphs
including scalar mesons, we use the octet baryon masses and the pion--nucleon
$\sigma$--term to fix all but one of these coefficients. Physical results are
insensitive to this remaining parameter. It is also demonstrated that two--loop
corrections only modify some of the subleading low--energy constants. We find
for the baryon mass in the chiral limit, $m_0 = 770 \pm 110$ MeV. While the
corrections of order $m_q^2$ are small for the nucleon, they are still sizeable
for the $\Lambda$, the $\Sigma$ and the $\Xi$. Therefore a definitive statement
about the convergence of three--flavor baryon chiral perturbation can not yet
be made. The strangeness content of the nucleon is $y = 0.21 \pm 0.20$. We also
estimate the kaon--nucleon $\sigma$--terms and some two--loops contributions to
the nucleon mass.
