Summary: Several mechanisms have been proposed to explain observed phenomenon in gas phase decompositions, yet few theoretical solutions exist. One set of simple mechanisms is proposed by Christiansen and Lindemann [\textit{K. J. Laidler}, Chemical Kinetics, McGraw-Hill, New York (1950), pp. 76-85], which can be modeled as follows: (i) \(A+A\rightleftharpoons A^*+A\), (ii) \(A+M\rightleftharpoons A^*+M\), (iii) \(A^*\to P\), where \(A\) represents a normal reactant molecule, \(A^*\) an activated \(A\) molecule, \(M\) an inert substance, and \(P\) the decomposition products. In this mechanism, an \(A\) molecule can be activated by collision with another \(A\) molecule (step (i)) or an inert molecule \(M\) (step (ii)). The activated molecule can deactivate by a collision with an \(A\) or \(M\) molecule (steps (i) or (ii)) or decompose to form products (step (iii)). This scheme is modeled by a nonlinear set of ordinary differential equations. This paper shows that under normal laboratory conditions these equations can be treated as weakly nonlinear. Perturbation solutions are derived and conclusions given.