We consider linear differential equations of the form F(x, z)≡ xn + a1(z)x(n-1)+…+an(z)x = 0 with power-logarithmic coefficients or coefficients which are asymptotically similar to power-logarithmic functions in a central sector S of a complex plane for z →∞, z∈S. The main result of this paper is that in a sufficiently small central sector SE⊂S there is a fundamental system of solutions {xi(z) = exp [∫γi(z)dz)} where each function γi(z) is equivalent to a power-logarithmic function or has an estimate of the form O(z−∞). Furthermore, a precise estimate is obtained for a partial solution of a nonhomogeneous equation F(x, z) = α(z), where the function α(z) grows like a power.