Computer inversion of measurement data based on the equation of particle transport is a topical component of the modern nuclear-geophysical technologies. In this work we have elaborated an approach and iterative methods for this inversion according to the gamma-gamma method data. In the framework of the "successive approximations according to characteristic interactions" approach, characteristic interactions have been established and iterative methods for the solution of two problems have been developed, namely, the problem of evaluation of the formation density and the problem of evaluation of two parameters-the formation density and the mud cake thickness. The numerical experiments confirm the theoretical concepts on the properties of iterative processes and convergence of methods