We present the results of the spin asymmetries A1 of the proton and the deuteron in the kinematic region extending down to x=6×10-5 and Q2=0.01 GeV2. The data were taken with a dedicated low x trigger, which required hadron detection in addition to the scattered muon, so as to reduce the background at low x. The results complement our previous measurements and the two sets are consistent in the overlap region. No significant spin effects are found in the newly explored region. ©1999 The American Physical Society.