We present high-resolution Magellan/MIKE spectra of 22 bright (9<V<13.5) metal-poor stars (-3.18<[Fe/H]{<}-1.37) in three different stellar streams, the Helmi debris stream, the Helmi trail stream, and the {omega} Centauri progenitor stream. We augment our Helmi debris sample with results for 10 stars by Roederer+ (2010, J/ApJ/711/573) for a total of 32 stars. Detailed chemical abundances of light elements as well as heavy neutron-capture elements have been determined for our 22 stars. All three streams contain carbon-enhanced stars. For 13 stars, neutron-capture element lines were detectable, and they all show signatures in agreement with the scaled solar r-process pattern, albeit with a large spread of -0.5<[Eu/Fe]<+1.3. Eight of these stars show an additional small s-process contribution superposed onto their r-process pattern. This could be discerned because of the relatively high signal-to-noise ratio of the spectra given that the stars are close by in the halo. Our results suggest that the progenitors of these streams experienced one or more r-process events early on, such as a neutron star merger or another prolific r-process source. This widely enriched these host systems before their accretion by the Milky Way. The small s-process contribution suggests the presence of asymptotic giant branch stars and associated local (inhomogeneous) enrichment as part of the ongoing chemical evolution by low-mass stars. Stars in stellar streams may thus be a promising avenue for studying the detailed history of large dwarf galaxies and their role in halo assembly with easily accessible targets for high-quality spectra of many stars.