The effect of hydrostatic pressure and partial Na substitution on the normal-state properties and the superconducting transition temperature (Tc) of K1−xNaxFe2As2 single crystals were investigated. It was found that a partial Na substitution leads to a deviation from the standard T 2 Fermi-liquid behavior in the temperature dependence of the normal-state resistivity. It was demonstrated that non-Fermi liquid like behavior of the resistivity for K1−xNaxFe2As2 and some KFe2As2 samples can be explained by disorder effect in the multiband system with rather different quasiparticle effective masses. Concerning the superconducting state our data support the presence of a shallow minimum around 2 GPa in the pressure dependence of Tc for stoichiometric KFe2As2. The analysis of Tc in the K1−xNaxFe2As2 at pressures below 1.5 GPa showed, that the reduction of Tc with Na substitution follows the Abrikosov-Gor'kov law with the critical temperature Tc0 of the clean system (without pair-breaking) which linearly depends on the pressure. Our observations, also, suggest that Tc of K1−xNaxFe2As2 is nearly independent of the lattice compression produced by the Na substitution. Further, we theoretically analyzed the behavior of the band structure under pressure within the generalized gradient approximation (GGA). A qualitative agreement between the calculated and the recently in de Haas-van Alphen experiments 1 measured pressure dependencies of the Fermi-surface cross-sections has been found. These calculations, also, indicate that the observed minimum around 2 GPa in the pressure dependence of Tc may occur without a change of the pairing symmetry.