The first‐ and the second‐order Bragg interactions in an unbounded active medium having a sinusoidally varying permittivity or gain in the direction of progression of the interacting waves are investigated. In the first‐order Bragg interaction, there is absolute instability of the participating waves. In the second‐order Bragg interaction, the waves are convectively unstable with their spatial amplification reduced in the Bragg region by the destructive interference of the two interacting waves. The nature of these instabilities are analyzed and physical explanations for the various characteristics are provided. When the gain of the medium is an order magnitude smaller than the modulation index, the absolute instability, instead of taking place in the first, occurs, in the second Bragg region. The importance of incorporating the gain in a manner that is consistent with the material dispersion law is emphasized.