A simple method of construction of linearized kinetic models is proposed which is based upon the equivalence of moments of theNth‐order modeled collision operator and the moments of the full collision operator calculated with theNth‐order approximation to the distribution function. This method is used to construct a third‐order model of the linearized cross‐collision operator for a general multicomponent monatomic gaseous mixture, not restricted to Maxwell molecules. In addition, this method is used to extend the Hanson‐Morse diatomic gas model of the Wang Chang‐Uhlenbeck collision operator to a polyatomic gas. Also presented is a new method of formally extending the Gross‐Jackson modeling procedure to multicomponent monatomic mixtures. It is shown that the method of constructing mixture models based on the equivalence of moments is identical to this new procedure. In addition, the Gross‐Jackson modeling procedure recently developed for mixtures by Boley and Yip is analyzed. It is shown that, under a certain weak restriction, their method is equivalent to the simpler Gross‐Jackson procedure — and leads to the same expression for theNth‐order model, except for the manner of specification of the constant in the diagonal approximation.