We present the final results of the spin asymmetries A(1) and the spin structure functions g(1) of the proton and the deuteron in the kinematic range 0.0008 < x < 0.7 and 0.2 < Q(2) < 100 GeV2. For the determination of A(1), in addition to the usual method which employs inclusive scattering events and includes a large radiative background at low x, we use a new method which minimizes the radiative background by selecting events with at least one hadron as well as a muon in the final state. We find that this hadron method gives smaller errors for x < 0.02, so it is combined with the usual method to provide the optimal set of results. [S0556-2821(98)07017-9].