We report results from studies of baryon ground and resonant states by taking explicit mesonic degrees of freedom into account. We are following a relativistic coupled-channels approach relying on a Poincaré-invariant mass operator in matrix form. Generally, it corresponds to a bare particle that is coupled to a number of further mesonic channels. Here we present results, where the bare particle is either a bare nucleon or a bare Delta coupled to pion-nucleon and pion-Delta channels, respectively. For the pion-baryon vertices we employ coupling constants and form factors from different models in the literature. From the mass-operator eigenvalue equation we obtain the pion-dressing effects on the nucleon mass as well as the mass and pion-decay width of the Delta. The dressed masses become smaller than the bare ones, and a finite width of the Delta is naturally generated. The results are relevant for the construction of constituent-quark models for baryons, which have so far not included explicit mesonic degrees of freedom, but have rather relied on three-quark configurations only.A proper description of hadron resonances poses considerable problems in all current approaches to quantum chromodynamics (QCD). Along constituent-quark models resonances have hitherto usually been considered as excited bound states rather than as genuine resonances with finite decay widths. Covariant predictions for decay widths of baryons have shown shortcomings usually underestimating data from phenomenology [1][2][3][4]. A possible remedy consists in coupling to decay channels and thereby including mesonic degrees of freedom explicitly.In this spirit we construct a relativistically invariant coupled-channels (CC) mass operatorHerein MB is the mass operator of a bare particleB, which in our case is either a bare nucleonÑ or a bare DeltaΔ. The second channel with the mass operator MB +π contains in addition an explicit interaction-free π.The transition between the channels is governed by the operator K . The mass eigenvalue m B becomes real for the physical nucleon N (no decay channel open) and complex for the physical Delta Δ (as a genuine resonance acquiring a finite decay width).