The problem of modelling critically linear systems with product non-linearity is considered. A new linearization technique is proposed using mathematical perturbation methods. The class of systems considered is represented by an extended linear state space model. An upper bound on the order of the developed model is obtained. Conditions of asymptotic stability are derived and it is shown that the model, under the appropriate conditions, is observable provided the unperturbed part of the nonlinear system is observable.