The stability problem for point kinetics models described by a set of nonlinear differential equations is treated by conversion to a set of Volterra integral equations. The kernels appearing in the resultant set are classified as to monotone behavior and comparison theorems are presented for the various classifications. The comparison theorems are utilized to calculate solution bounds and stability domains for three systems of practical interest: prompt power feedback, single temperature with prompt power coefficient, and the Hansen-Fuchs model. It is shown that similarity transformations are useful for enlarging the stability domain. An iteration procedure is also developed for a particular class of integral operators. This procedure is useful for finding convergent bounds for the true system behavior.