  This paper presents an iteration method for solving linear particle transport
problems in binary stochastic mixtures. It is based on nonlinear projection
approach. The method is defined by a hierarchy of equations consisting of the
high-order transport equation for materials, low-order Yvon-Mertens equations
for conditional ensemble average of the material partial scalar fluxes, and
low-order quasidiffusion equations for the ensemble average of the scalar flux
and current. The multilevel system of equations is solved by means of an
iterative algorithm with the $V$-cycle. The iteration method is analyzed on a
set of numerical test problems.
