Experiments were performed on an atmospheric pressure glow discharge (APGD) in an air gap between two dielectric barrier electrodes. While it is possible to get an APGD in a 2mm air gap, it is possible to get only a filament discharge in a 5mm air gap. The development of an electron avalanche in such a gap was numerically simulated. It was found that the critical applied field for a 5mm electron avalanche to transit to a streamer is equal to 35.07kVcm-1. This calculated critical applied field is in good agreement with the experimental one. The experimental and theoretical results confirm that only a filament discharge, rather than a glow discharge, can be produced in an atmospheric pressure air gap that is not less than 5mm if it is not possible to lower the breakdown field of air. A resistive barrier discharge (RBD) was theoretically analysed and the development of RBD was numerically simulated. If a kilohertz discharge is required, the parameters of the resistive layer should be in the rangeρεr=(109-1011)Ωcm. APGD in a helium gap was realized using 50Hz line power with a suitably fabricated resistive layer.