 BKL further developed a matter distribution-independent model (homogeneous or non-homogeneous) for long era with small oscillations.The time dependence of this solution turns out to be very similar to that in the particular case of homogeneous models; the latter can be obtained from the distribution-independent model by a special choice of the arbitrary functions contained in it.It is convenient, however, to construct the general solution in a system of coordinates somewhat different from synchronous reference frame