Lattice-parameter (a(0)(ss)) data of defect-fluorite M(1-y)Ln(y)O(2-y/2) solid solutions (ss) (M4+ = Ce, Th; Ln(3+) = Y, Gd, Eu, Sm, Nd, La) exhibit markedly positive deviations from Vegard's law, systematically larger in M4+ = Th than Ce. A detailed analysis elaborates upon a previous a(0)(ss) model [1,2] and clarifies the 'generalized non-Vegardian' behavior of oxygen-vacancy (V-O) type 'distortionally dilated' MO2-LnO(1.5) solid solutions with non-random oxygen coordination around the cations of CN(Ln(3+))not equal CN(M4+). M4+ = Ce and Th are similarly modestly Ln(3+)-V-O associative (CN(Ln(3+)) non-random model extension and major a(0) (ss)-analysis results that include a comparison with the reported local-structure, thermodynamic and ionic-conductivity data from these systems. Several basic concepts and premises of the present model are also discussed, paving the way to a detailed local-structure analysis of the systems in Part II. (C) 2010 Elsevier B.V. All rights reserved.