  Given the existing empirical information about the exotic Theta+ baryon, we
analyze possible properties of its SU(3)F-partners, paying special attention to
the nonstrange member of the antidecuplet N*. The modified piN partial-wave
analysis presents two candidate masses, 1680 MeV and 1730 MeV. In both cases,
the N* should be rather narrow and highly inelastic. Our results suggest
several directions for experimental studies that may clarify properties of the
antidecuplet baryons, and structure of their mixing with other baryons. Recent
experimental evidence from the GRAAL and STAR Collaborations could be
interpreted as observations of a candidate for the Theta+ nonstrange partner.
