[en] Absolute differential cross sections for elastic αp scattering and the sum of elastic and quasielastic αα scattering have been measured with a normalization error no more than 3% for α particles with momentum 17.9 GeV/c in the interval of squared 4-momentum transfers 0.01< Vertical Bar t Vertical Bar<0.02 (GeV/c)₂. These measurements in the energy region of several GeV/nucleon are made for the first time. We have determined total cross sections, diffraction-peak slope parameters, and total elastic cross sections for αp and αα scattering. The data are compared with calculations carried out in the framework of the Glauber-Sitenko diffraction theory of multiple scattering. A deviation of the calculated differential cross sections from the experimental values is observed; in the region of the diffraction peak it amounts to 10--15% and has different signs for αp and αα scattering