A simplified theory of Gunn domains is presented assuming a nonzero, but field‐independent diffusion coefficient. The simplification is achieved by using an approximate, analytic solution to a well‐known transcendental equation (the so‐called ``area integral'') of Butcher and Fawcett. Any further computer calculations, where necessary, then involve only simple quadratures of known analytic functions. For the piece‐wise linear approximation to theV(F) vsFcurve the entire program can be carried out analytically with the aid of the Regional Approximation method. The use of dimensionless variables brings out the central role, in Gunn domain theory, of the critical dimensionless parameter &agr;=&egr;FTVT/eN0D, withFTthe threshold field,VTthe threshold drift velocity,N0the thermal‐equilibrium free‐carrier density andDthe diffusion coefficient (mks formula). For GaAs, &agr;≈4×1015/N0withN0in cm−3. A particularly simpleV(F) vsFcurve is proposed for the study of phenomena (e.g., impact ionization across the gap) deriving from very high‐field Gunn domains. A complete analytic study is made of the Gunn domains associated with this special characteristic.