  A fully non-perturbative lattice determination of the up/down and strange
quark masses is given for quenched QCD using both, $O(a)$ improved Wilson
fermions and ordinary Wilson fermions. For the strange quark mass with $O(a)$
improved fermions we obtain $m^{\msbar}_s(\mu=2 {GeV}) = 105(4) {MeV}$, using
the interquark force scale $r_0$. Due to quenching problems fits are only
possible for quark masses larger than the strange quark mass. If we extrapolate
our fits to the up/down quark mass we find for the average mass
$m^{\msbar}_l(\mu=2 {GeV}) = 4.4(2) {MeV}$.
