A dispersion functional for the Vlasov‐fluid model is derived as a finite‐Larmor‐radius (FLR) expansion in which the eigenfrequency is not assumed to be small compared to the ion gyrofrequency and secularities in the gyrophase angle never occur. The expansion is carried out in the localE0×B0drift frame. Use of the dispersion functional for calculating the small‐signal response of a plasma is compared to using an approximate dispersion differential equation. The linearized Vlasov‐fluid model is examined with particular reference to the questions of treating the initial‐value problem correctly and specifying a generally valid gauge condition. Calculational details for applying the dispersion functional to a general linear screw pinch are presented.