AbstractThe problem of adiabatic excursions in a reactor is studied in general. We let the prompt temperature reactivity feedback be an unspecified function of temperature,ρ=ρ0=ρ0+ f(T), whereρis total reactivity,ρ0initial step reactivity andf(T)the feedback function. The similarity of the behavior of the reactor for differentf(T)is established by means of a topological (qualitative) analysis. A quantitative asymptotic solution of the non-linear system ofDEdescribing the reactor is presented. In delayed critical excursions, the delayed neutrons play a determining role. In the first part of a prompt excursion, the delayed-neutron source is nil; however this is not so in the second part, where it contributes appreciably to the excursion. These conclusions are shown to be valid in general, and allow us to write down almost directly the (approximate) quantitative solution of the non-linear system forany f(T). These results are correlated with the experimental data for the adiabatic excursions of a UO2core in SPERT I; in this case the (prompt) dependence of the reactivity on energy is of the formρ=ρ0- 4.588×10-4E0.74.