The paper investigates the properties of general reduced order models obtained by projection of a higher order system. It answers questions such as, are any two models of different orders related by a projection? Is it possible to obtain the same reduced order model using different projections? How to find, if it exists, a projection that relates the two models?, etc. It is shown that answers to those questions can be obtained by investigating the properties of a certain matrix pencil. The key tool is the Kronecker canonical form, and in some cases of square systems the problem becomes that of generalized eigenvalues. (c) 2006 Elsevier Ltd. All rights reserved.