  We study the spectrum of light flavor baryons in a quark-model framework by
taking into account the order $\mathrm{O}(\alpha_s^2)$ hyperfine interactions
due to two-gluon exchange between quarks. The calculated spectrum agree better
with the experimental data than the results from hyperfine interactions with
only one-gluon exchange. It is also shown that two-gluon exchange hyperfine
interactions bring a significantly improved correction to the Gell-Mann--Okubo
mass formula. Two-gluon exchange corrections on baryon excitations (including
negative parity baryons) are also briefly discussed.
