Spin glasses in dimensions 2, 3, 4 and mean field are studied numerica
lly as a function of the degree of asymmetry of the interactions betwe
en spins. Damage spreading data are used to assess the effects on the
spin glass ordering of introducing asymmetry in the couplings. In all
dimensions the critical temperature for damage spreading is rather ins
ensitive to the asymmetry, but the spin glass ordering is strongly sup
pressed by any finite degree of asymmetry. We discuss the physical sig
nificance of the damage spreading parameter.