A technique is presented for the analysis of thermal stability in reacting tokamak plasmas using a one-dimensional, time-dependent fluid transport model. Application is made to the analysis of density-related thermal instabilities in a neutral-beam-driven, two-component plasma (TETR) and a conceptual reactor-size ignited plasma (UWMAK-III). A density-driven thermal instability can exist when the particle confinement varies as τp ∝ n. This condition is satisfied by the trapped-ion-mode diffusion model and an empirical model. A time delay in the heating due to finite alpha thermalization does not significantly alter the character of the instability at normal plasma densities. A linear feedback response for the particle source is found to provide a stabilized equilibrium in all cases. Strong radial variation of the transport and physical properties of the plasma is not found to introduce radial-dependent feedback requirements. Feedback on the average density is sufficient for stabilization with moderate response times.