In the present paper, we continue the study of the asymptotic properties of the form factors of deep inelastic lepton-hadron scattering by the method proposed by Bogolyubov, Vladimirov, and Tavkhelidze [11. This method, which is based on the use of the Jost-Lehmann-Dys on repiresentation, has proved very fruitful. In particular, it has been shown that power-law asymptotic behaviors in the Bjorken region do not contradict the general principles of quantum field theory. On the other hand, combining this method with the idea of the quasiasymptotic behavior of generalized functions [2-4] it has proved possible to establish rigorously a one-to-one correspondence between Bjorken asymptotic behavior, the singularities of the current commutators in the neighborhood of the light cone, and the asymptotic properties of the spectral function in the JostLehmann-Dyson representation. In this connection, there arises the interesting problem of describing the complete class of asymptotic behaviors permitted by the general principles of field theory (i. e., that do not contradict them). Let us say right away that this problem is not completely solved in the present paper. Instead, we first extend the class of permitted asymptotic behaviors by including in it not only power-law behavior but also generalized power-law behavior (or, as we shall call this in what follows, self-similar asymptotic behavior). * Second, we show that asymptotic behaviors that in a certain sense differ little from self-similar behaviors but are not do contradict the general principles of field theory. In this way we show that the general principles of field theory alone, which any realistic theory must satisfy, already impose certain restrictions on the asymptotic behavior of the deep inelastic scattering form factors. Since self-similar functions will, as we hav e already noted, play an essential role in what follows, it will be expedient to recall some facts relating to these functions. All the proofs and further properties can be found, for example, in the book [6] (Appendix 1). DEFINITION 1. Let p(t) be a positive function defined on the positive half-axis. We shall say that p(t) is asymptotically self-similarr (or, for brevity, simply self-similar) if for any a > 0 there exists the limit