Transient solutions of a nonlinear nuclear reactor with various temperature-dependent feedbacks are obtained by the modified Newton-Raphson-Kantorovich’s iterative technique. The difference between the first and higher iterates is shown explicitly to be negligible at all times, so that the first iterate represents well the entire solution. It is also shown that the spatial distribution of the neutron flux during transience is dominated by the fundamental mode and that the negligible difference between the second and the first iterates is composed of higher harmonics.—, The maximum flux, the time at which it occurs, and the rate of flux increase are all readily obtained from the solutions. For an increase in reactor buckling and for a positive initial flux disturbance, the neutron flux in a reactor with Newtonian or prompt feedback reaches a finite asymptotic value, whereas that of an adiabatic reactor first rises, then drops off. However, for the same initial conditions, the maximum flux attained in an adiabatic reactor is several fold higher than that of a reactor with Newtonian or prompt feedback.