We studied the dynamics of synchronization in asymmetrically coupled neural oscillators with time delay. Stability analysis revealed that symmetric excitatory coupling results in synchrony at multiple phase relations. Asymmetry yields two saddle-node bifurcations of the stable states when coupling is asymmetric. By contrast, with inhibitory coupling only in phase or antiphase is stable as long as coupling is symmetric. Otherwise, these stable states shift or even vanish. The reduced bistability range suggests the beneficial role of asymmetric coupling for reliable neural information transfer.