We investigate the properties of compressed and hot hadronic matter within the Non-Linear Derivative (NLD) formalism. The novel feature of the NLD model is an explicit momentum dependence of the mean-fields, which is regulated by cut-off’s of natural hadronic scale. It is covariantly and thermodynamical-consistently formulated at the basis of a field-theoretical level. We show that the NLD model describes adequately all the empirical information of cold nuclear matter as function of density (equation of state) and, in particular, as function of particle momenta (optical potential). Finally, we present predictions of the NLD approach for hot and compressed hadronic matter in terms of the Equation of state as function of density and temperature. These studies are relevant for the forthcoming experiments at FAIR@GSI. They are also important for astrophysical purposes, e.g., static neutron stars and dynamic neutron star binary systems.