We present abundances for 20 elements for stars in two stellar streams identified by Arifyanto & Fuchs: 18 stars from the Arcturus stream and 26 from a new stream, which we call the AF06 stream, both from the Galactic thick disc. Results show that both streams are metal poor and very old (10–14 Gyr) with kinematics and abundances overlapping with the properties of local field thick-disc stars. Both streams exhibit a range in metallicity but with relative elemental abundances that are identical to those of thick-disc stars of the same metallicity. These results show that neither stream can result from dissolution of an open cluster. It is highly unlikely that either stream represents tidal debris from an accreted satellite galaxy. Both streams most probably owe their origin to dynamical perturbations within the Galaxy.