First measurement of the beam asymmetry $Sigma$ for Compton scattering off the proton in the energy range $E_{gamma}=0.85 - 1.25$ GeV is presented. The data reveals two narrow structures at $E_{gamma}= 1.036$ and $E_{gamma}=1.119$ GeV. They may signa
l narrow resonances with masses near $1.68$ and $1.72$ GeV, or they may be generated by the sub-threshold $KLambda$ and $omega p$ production. Their decisive identification requires additional theoretical and experimental efforts.
The first study of quasi-free Compton scattering on the neutron in the energy range of $E_{gamma}=0.75 - 1.5$ GeV is presented. The data reveals a narrow peak at $Wsim 1.685$ GeV. This result, being considered in conjunction with the recent evidence
for a narrow structure at $Wsim 1.68$GeV in the $eta$ photoproduction on the neutron, suggests the existence of a new nucleon resonance with unusual properties: the mass $Msim 1.685$GeV, the narrow width $Gamma leq 30$MeV, and the much stronger photoexcitation on the neutron than on the proton.
