This work is devoted to the formulation and derivation of the $η{-}μ{/}$gamma and $λ{-}μ{/}$gamma distributions which correspond to physical fading models. These distributions are composite and are based on the $η-μ$ and $λ-μ$ generalized multipath models, respectively, and the gamma shadowing model. Novel analytic expressions are derived for the corresponding envelope probability density functions. Importantly, the proposed models provide accurate characterisation of the simultaneous occurrence of multipath fading and shadowing effects which is achieved thanks to the remarkable flexibility offered by their parameters that render them capable of providing good fittings to experimental data associated with realistic communication scenarios. This is additionally justified by the fact that they include as special cases the widely known fading models such as Hoyt/gamma, Nakagami-m/gamma and Rayleigh/gamma. As a result, they can be meaningfully utilized in various analytical studies related to the performance evaluation of digital communications over composite multipath/shadowing fading channels.