[en] We have measured the proton and deuteron spin structure functions g₁^p and g₁^d in the region of the nucleon resonances for W² < 5 GeV² and Q² ≅ 0.5 and Q² ≅ 1.2 GeV² by inelastically scattering 9.7 GeV polarized electrons off polarized ¹⁵NH₃ and ¹⁵ND₃ targets. We observe significant structure in g₁^p in the resonance region. We have used the present results, together with the deep-inelastic data at higher W², to extract Γ(Q²) (triple_bond) ∫₀¹ g₁(x,Q²) dx. This is the first information on the low-Q² evolution of Gamma toward the Gerasimov-Drell-Hearn limit at Q² = 0