The embedding theorems in anisotropic Besov-Lions type spaces B-p,theta(l)(R-n; E-0, E) are studied; here E-0 and E are two Banach spaces. The most regular spaces Ea are found such that the mixed differential operators D-alpha are bounded from B-p,theta(l)(R-n; E-0, E) to B-q,theta(s)(R-n; E-alpha), where E-alpha are interpolation spaces between E-0 and E depending on alpha = (alpha(1), alpha(2),..., alpha(n)) and l = (l(1), l(2),..., l(n)). By using these results the separability of anisotropic differential-operator equations with dependent coefficients in principal part and the maximal B-regularity of parabolic Cauchy problem are obtained. In applications, the infinite systems of the quasielliptic partial differential equations and the parabolic Cauchy problems are studied. Copyright (C) 2006 Veli B. Shakhmurov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.