Expressions for neutron and gamma factorial momentshave been known in the literature. The neutronfactorial moments have served as the basis of constructinganalytic expressions for the detection ratesof singles, doubles and triples, which can be used tounfold sample parameters from the measured neutronmultiplicity rates. The gamma factorial momentscan also be extended into detection rates of multiplets,as well as the combined use of joint neutronand gamma multiplicities and the corresponding detectionrates. Counting up to third order, there arenine auto- and cross factorial moments.Adding the gamma counting to the neutrons introducesnew unknowns, related to gamma generation,leakage, and detection. Despite of having more unknowns,the total number of independent measurablemoments exceeds the number of unknowns. On theother hand, the structure of the additional equationsis substantially more complicated than that of theneutron moments, hence the analytical inversion ofthe gamma moments alone is not possible.We suggest therefore to invert the non-linear systemof over-determined equations by using artificialneural networks (ANN), which can handle both thenon-linearity and the redundancies in the measuredquantities in an effective and accurate way. The useof ANN is successfully demonstrated on the unfoldingof neutron multiplicity rates for the sample fissionrate, the leakage multiplication and the ratio.The analysis is further extended to unfold also thegamma related parameters. The stability and robustnessof the ANNs is further investigated to verify theapplicability of the method. The ANN approach enablesextraction of additional important informationon the fissile sample compared to the application ofthe analytical method.