Context : The rapid neutron-capture process , which created about half of the heaviest elements in the solar system , is believed to have been unique . Many recent studies have shown that this uniqueness is not true for the formation of lighter elements , in particular those in the atomic number range 38 < Z < 48 . Among these , palladium ( Pd ) and especially silver ( Ag ) are expected to be key indicators of a possible second r-process , but until recently they have been studied only in a few stars . We therefore target Pd and Ag in a large sample of stars and compare these abundances to those of Sr , Y , Zr , Ba , and Eu produced by the slow ( s- ) and rapid ( r- ) neutron-capture processes . Hereby we investigate the nature of the formation process of Ag and Pd . Aims : We study the abundances of seven elements ( Sr , Y , Zr , Pd , Ag , Ba , and Eu ) to gain insight into the formation process of the elements and explore in depth the nature of the second r-process . Methods : By adopting a homogeneous one-dimensional local thermodynamic equilibrium ( 1D LTE ) analysis of 71 stars , we derive stellar abundances using the spectral synthesis code MOOG , and the MARCS model atmospheres . We calculate abundance ratio trends and compare the derived abundances to site-dependent yield predictions ( low-mass O-Ne-Mg core-collapse supernovae and parametrised high-entropy winds ) , to extract characteristics of the second r-process . Results : The seven elements are tracers of different ( neutron-capture ) processes , which in turn allows us to constrain the formation process ( es ) of Pd and Ag . The abundance ratios of the heavy elements are found to be correlated and anti-correlated . These trends lead to clear indications that a second/weak r-process , is responsible for the formation of Pd and Ag . On the basis of the comparison to the model predictions , we find that the conditions under which this process takes place differ from those for the main r-process in needing lower neutron number densities , lower neutron-to-seed ratios , and lower entropies , and/or higher electron abundances . Conclusions : Our analysis confirms that Pd and Ag form via a rapid neutron-capture process that differs from the main r-process , the main and weak s-processes , and charged particle freeze-outs . We find that this process is efficiently working down to the lowest metallicity sampled by our analysis ( [ Fe/H ] = - 3.3 ) . Our results may indicate that a combination of these explosive sites is needed to explain the variety in the observationally derived abundance patterns .