The strengthening effect of twins in nanocrystalline metals has been reported both in experiment and simulation. While twins are mostly considered as effective barriers to dislocation slip transfer, they can also provide nucleation sites for dislocations or migrate during the deformation process, thereby contributing to plasticity. By comparing twinned and nontwinned samples, we study the effect of twins on the deformation behavior of nanocrystalline Cu and Pd using atomistic simulations. While Cu shows hardening due to the presence of twins, Pd shows the opposite effect. A quantitative dislocation analysis method is applied, which allows to analyze dislocation interactions with twin planes and grain boundaries and to measure dislocation, stacking fault, and twin-boundary densities as functions of strain. A statistical analysis of the occurring dislocation types provides direct evidence for the role of twin boundaries as effective sources for twinning dislocations, which are the reason for the observed softening in some fcc materials. In addition, we discuss how the orientation of the loading direction with respect to the twin planes affects the response of nanotwinned Cu and Pd.