Identifiability and distinguishability are essential uniqueness features of reaction schemes. Identifiability deals with the problem of determining whether an experiment is able to supply the desired information on the parameters of a model, whereas distinguishability examines the uniqueness of a kinetic model itself within a given class of competing models. Deterministic analysis, assuming error-free and continuous knowledge of measurable quantities, is a useful first step toward establishing uniqueness properties, because deterministic identifiability (distinguishability) is a necessary condition for their existence in any realistic experiment. Deterministic uniqueness conditions have been described in the literature only for first-order reaction systems. This paper extends the method to isothermal systems that include reactions of arbitrary order with mass-action-type rate equations. In contrast to the first-order case with relatively simple examples of unidentifiable and/or undistinguishable systems, all higher order schemes we have studied turned out to be both identifiable and distinguishable from other schemes in a deterministic sense when consideration is restricted to reasonable kinetic experiments. In principle, an identifiable and distinguishable model can be uniquely and completely reconstructed from observable quantities such as the concentrations of stable species, provided that these functions are known continuously and are error-free. In many cases, however, the presence of measurement noise and limitations on the sampling rate make unique reconstruction not possible. Nevertheless, since unidentifiability and indistinguishability of higher order kinetic schemes are of numerical rather than of deterministic origin, the difficulties can be controlled to a certain degree by improving the design of experiments and by raising measurement accuracy.