An Spiking Neural P system with anti-spikes uses two types of objects called spikes and anti-spikes which can encode binary digits in a natural way. The step when system emits a spike or an anti-spike is associated with symbol 1 and 0, respectively. Here we consider these computing devices as language generators. They allow non-determinism between the rules ac → a and ac → a-, c ε N, thus help to generate languages which cannot be generated using simple SN P systems. © 2011 World Scientific Publishing Company.