Jacquet modules are very useful in the study of parabolically induced representations of reductive groups over a p-adic field F (we shall assume char F = 2 in this paper). It is very hard to describe explicitly the structure of Jacquet modules of parabolically induced representations, particularly in the most interesting cases. There exists a description of factors of certain filtrations on them. That description was done by J. Bernstein and A. V. Zelevinsky in [BZ2], and by W. Casselman in [C]. In the case of general linear groups, the functor of parabolic induction and the Jacquet functor induce a structure of Z+-graded Hopf algebra on the sum R of Grothendieck groups of categories of smooth representations of GL(n, F )’s of finite length, n ≥ 0 ([Z1]). The multiplication m : R × R → R is defined using parabolic induction, while the comultiplication m∗ : R → R ⊗ R is defined in terms of Jacquet modules. The most interesting part of the structure is the property that m∗ : R → R⊗R is a ring homomorphism (Hopf axiom). This enables one to compute composition series of parabolically induced representations in a very simple way. It is interesting to note that the existence of this strong structure did not have serious impact on the development of the representation theory of GL(n, F ). One of the reasons for that may lay in the fact that for GL(n, F ) there existed a very powerful theory of GelfandKazhdan derivatives, and the main results of [Z1] were obtained using them. Nevertheless, A.V. Zelevinsky showed in [Z2] that some interesting parts of the representation theory of GL(n) over a finite field can be obtained as a structure theory of such Hopf algebra (defined in this setting). Besides that, one of the main tools for the study of representation theory of GL(n) over a central division F -algebra in [T1] is such Hopf algebra structure (in this situation are not available Gelfand-Kazhdan derivatives). It is natural to ask does some structure of this kind exist for other (simple split) classical p-adic groups. Since Levi factors of classical groups are isomorphic to direct products of general linear groups and smaller groups from the same series, one can expect for such structure to have some relation with R (if it exists). In the third section we define the direct sum of Grothendieck groups R(S), which corresponds either to the series Sp(n, F ), n ≥ 0, or SO(2n+ 1, F ), n ≥ 0, in a similar way as R was defined for general linear groups. The action of R on R(S) is defined using the parabolic induction. In this way R(S) becomes Z+-graded R-module. We can make R(S) a Z+-graded comodule over R. The comodule structure map μ∗ : R(S) → R⊗R(S) is again defined using the Jacquet modules, similarly as in the case of GL(n, F ). It is not hard to see that R(S) is not a Hopf module over R (see Remark 7.3). In this paper we