In the last two years a large number of iron based compounds with relatively high temperature of the superconducting transition have been synthesized. Among them there such compounds as ReOFeAs (Re=La,Ce,Na, Sm, …), AFe2As2 (A=Ba, Sr, …) and some. The record of the observed transition temperature in such compounds is 56 K [1,2]. This novel class of materials, besides existing cuprate-based high-Tc superconductors, provides yet another system for exploring the interplay between superconductivity and antiferromagnetism. The account of the band structure (peculiar properties in the electron energy spectrum) is of great importance in the theoretical study of thermodynamic and kinetic properties of these materials. In particularly, among such peculiar properties are multiband energy spectrum of electrons, presence of nesting, and also detailed structure of the Fermi surface of each considered compound. All these compounds posses layered structure and can be considered as quasi-two-dimensional systems with overlaps of several energetical bands on the Fermi surface. From a general point of view, this situation is not new and was examined repeatedly (see, eg, [3]). The main task is to find mechanisms, which lead to the appearance of the superconductivity on an antiferromagnetic background or adjacent to it. This work is devoted to the mentioned task. We have focused on the transition of the systems in the commensurate spin density wave (SDW) state with a subsequent phase transition into the incommensurate spin density wave state (ISDW) at the increasing of the density of carriers as a result of doping. The method of implementation of the summation by the impulse in the basic equations of the theory taking into account the Umklapp processes was elaborated. The resulting equation for the order parameter M of the magnetic phase also contains the order parameter h which characterizes the incommensurate spin density wave state. A system of equations for determining the values of M, h and TM, as well as the difference of free energies are obtained using Green function method. We have determined the dependence of the magnetic transition temperature TM on the value of chemical potential m . We have calculated the value of m c , for which there exists a solution of equations with = + ¹ 0 a b h h h , which corresponds to the stabilization of SDW. The emergence of a solution with h ¹ 0 corresponds to the phase transition from commensurability to incommensurability state. This corresponds to the transition dielectric-semimetal. In this state, the dielectric gap is shifted towards the Fermi surface, as a result, there are free carriers capable of forming Cooper pairs. The dependence of h on m at T = TM was investigated. In addition, the dependence of the above variables on the concentration of substitutional impurity was determined. In contrast to the theory of isotropic quasi-two-dimensional system [4], this theory contains two components of the order parameter ( a h and b h ), as well as the principled possibility of the structural transition in the ISDW state (from the orthorhombic state a ¹ b to tetragonal a = b ).