  A searche for supernarrow dibaryons (SND) and exotic baryons with small
masses is reviewed. As a result of the study of the reaction pd->p+pX_1, three
narrow peaks at M_{pX_1}=1904, 1926, and 1942 MeV have been observed. The
analysis of the angular distributions of the protons from the decay of the pX_1
states showed that the peaks found can be explained as a manifestation of the
isovector SNDs, the decay of which into two nucleons is forbidden by the Pauli
exclusion principle. The observation of the peaks in the missing mass M_{X_1}
spectra at 966, 986, and 1003 MeV is an additional indication that the
dibaryons found are the SNDs. The possible interpretation of these peaks in the
M_{X_1} mass spectra and peaks observed in the reaction pp->pi^+pX at M_X=1004,
1044, and 1094 MeV as new exotic baryon states with small masses is discussed.
The mass equation has been constructed which is used to calculate the masses
and determine parities of the exotic baryons. The obtained values of the masses
are in a good agreement with the experimental data. Two new exotic baryon
states bellow the \pi production threshold have been predicted.
