be the linear manifold of all trajectories of system (1), and let N∗ be some subset of Nθ. Two parameter values θ and ξ are said to be indistinguishable on N∗ if Nθ ⊇ N∗ and Nξ ⊇ N∗ simultaneously. (In this case, we write θ N∗ ∼ ξ.) Following [1–3], we say that a system is globally distinguishable with respect to N∗ at a point θ if ξ N∗ ∼ θ for ξ ∈ Ω implies that ξ = θ. A system is said to be locally distinguishable with respect to N∗ at θ if in some neighborhood of V (θ) the relation ξ N∗ ∼ θ for ξ ∈ V (θ) implies that ξ = θ. A system is said to be structurally (locally or globally) distinguishable in Ω if it is distinguishable at all points θ ∈ Ω possibly except for a set of zero Euclidean measure. Distinguishability problems arise in the construction of mathematical models in economics [4], technology [5], and medicine [6] as one has to choose equations whose solutions exactly describe or approximate given sets of experimental data. Distinguishability plays the role of a necessary condition for the identifiability of parameters in an equation. Sufficient conditions for identifiability depend on the character of measurements and an identification method [7; 8, p. 195 of the Russian translation; 9]. Constructive conditions (that is, conditions that can be verified in finitely many arithmetic operations) for the distinguishability of system (1) of zero order p = 0 were obtained in [10] in the form of constraints imposed on the ranks of special submatrices in γ0(θ). Systems of zero order are used, in particular, in econometrics [4, p. 31 of the Russian translation]. The generalization to systems of order p ≥ 0 carried out in the present paper is based on results of [11], where equivalent transformations of systems (1) of order p ≥ 0 with arbitrary finite trajectory lengths N were considered; it was shown there that they are related to some algebra of polynomial matrices; the possibility of using the analytic techniques of the polynomial matrix algebra in the analysis of finite-difference systems (1) with finite N is justified without the use of Laplace type transformations. Stochastic versions of systems (1) with additive perturbations in the observable variables were considered in [9, 12]. Parameters θ and ξ of a stochastic system are indistinguishable if the distributions Pθ and Pξ of observed trajectories coincide almost everywhere in R. Results on distinguishability both in observations and in the equation discrepancy under stochastic perturbations were obtained in [13, 14], where the relationship with the deterministic case was indicated.