In this paper the methods developed in earlier papers are extended to solving the problem of radiative transfer in curved atmospheres, i.e., to solving the equation of transfer μ∂l/∂r+(1-μ 2 )/r 2 ∂l/∂μ=-κρI+½κρ∫ +1 -1 Idμ, where κρ is a function only of r. After outlining a general method for replacing this partial integrodifferential equation by an equivalent system of 2n linear equations in the nth approximation, the most convenient forms of the equations for the first two approximations are found. The equations of the second approximation for the astrophysically important case κρ∝ r -n (n>1) are explicitly solved and found to involve quadratures over Bessel functions of purely imaginary arguments. For the case n=2 the solutions have been found in their numerical forms. Finally, the physically interesting case of diffusion through a homogeneous sphere is also considered.