IN this paper, on the basis of some integral identities for the solutions of multi-group kinetic equations an algorithm is constructed for forming sets of partial differential equations in coordinate space for solving kinetic problems approximately. We call the equations so obtained P NI -equations (see [1], [2]), they can be used both in P-operations in the KP-method [1], [2], and also to construct finite difference analogs of the kinetic equation. The method by which the P NI -equations will be obtained can be called the generalized Galerkin method (see [3]); the P NI -equations for some problems of transport theory are a generalization of such methods, e.g. the method of spherical harmonics [4]-[6], the KP-method [7], the method of characteristics [8], [9], Evans' method [4], and the method of decomposition of the solution into Jacobian polynomials [1O]. With regard to the last method this paper indicates the necessity of a correspondence between the dimensionality of the space in which the problem is solved and the representative Jacobian polynomial. In the choice of the form of the P NI -equations there is a fair amount of arbitrariness; in particular we can confine ourselves to considering strongly elliptic sets of equations, although up to now the strong ellipticity of the equations of the method of spherical harmonics has not yet been proved. It is also known that the working out of numerical algorithms for the calculation of multi-dimensional transport problems has been retarded because of the absence of sufficiently good quadrature formulae for a sphere, which may be used for a good approximation of the kinetic equation with as dense a network as we please with respect to spatial and angular variables, in PWJ-equations this difficulty is in some measure removed; with the choice of the best divisions with regard to the angle, we can use the results of paper [11] for some problems. In the choice of P NI -equations we shall confine ourselves to considering the case with an isotropic dispersion indicatrix, although the algorithm for derivation put forward can obviously be extended to the case of a degenerate indicatrix. In this paper, on the basis of the P NI -equations, various finite difference analogs for the kinetic equations are obtained; the convergence is proved in corresponding spaces of solutions of P NI -equations and of their difference analogs to the solution of the kinetic equation.