The main purpose of this paper is to characterize the nonmonotonic inference relations that can be represented by preferential models in which distinct states never satisfy exactly the same formulae (``injective models''). The key tool is the author's concept of ``preferential orderings''. These are relations between formulae satisfying certain postulates, and being transitive are easier to work with than the nontransitive nonmonotonic inference relations themselves. They generalize the plausibility and expectation orderings studied by \textit{D. Lehmann} and \textit{M. Magidor} [``What does a conditional knowledge base entail?'', Artif. Intell. 55, 1-60 (1992; Zbl 0762.68057)] and \textit{P. Gärdenfors} and \textit{D. Makinson} [``Nonmonotonic inference based on expectations'', ibid. 65, 197-245 (1994)]. The author defines a one-one mapping between nonmonotonic inference relations satisfying certain basic postulates (the ``preferential inference relations'' of \textit{S. Kraus}, \textit{D. Lehmann} and \textit{M. Magidor} [``Nonmonotonic reasoning, preferential models and cumulative logics'', ibid. 44, 167-207 (1990; Zbl 0782.03012)]), and his ``preferential orderings''. With that correspondence, he is able to establish a condition that is sufficient in the general case, and necessary and sufficient in the case of a logically finite language, for a preferential inference relation to be representable by an injective preferential model. This result is then applied to the particular cases of ``disjunctively rational'' and ``rational'' inference relations, obtaining representation by injective preferential models satisfying appropriate conditions, in which moreover a state satisfies all formulae \(\beta\) with \(\alpha | \sim\beta\) only if it is minimal among the states satisfying \(\alpha\) (the converse of which holds by definition in all preferential models).