A direct iteration has been performed to obtain a simultaneous solution of the equations of line transfer in an expanding spherically symmetric atmosphere in the comoving frame with statistical equilibrium for a non-LTE, two-level atom. The solution converges in three or four iterations to an accuracy of 1 per cent of the ratio of the population densities of the two levels. As initial values, the upper level population was set equal to zero or to the LTE densities. The final solution on convergence indicates enhanced population of these levels over the initial values assumed, Large velocity gradients enhance this effect whereas large geometrical sizes of the atmospheres tend to reduce it.