  We evaluate lower bounds on the sum of the up and down quark masses. The
bounds follow from the constraints provided by the dispersion relation obeyed
by the two--point function of the scalar current density when combined with
properties of the scalar spectral function at long--distances and perturbative
QCD at short--distances. Our results point to values of $m_u+m_d$ somewhat
higher than those reported recently in the literature using lattice QCD
simulations.
