Differential scattering cross sections were measured for fine-structure-inelastic collisions of potassium in its first excited state with various rare gases (Ne, Ar, Kr, and Xe). This crossed-mol.-beams expt. used cw-dye lasers for excitation of the incident potassium beam, and detection of the fine-structure-inelastic-scattered potassium atoms. The collision energy was varied between 92 and 199 meV. The differential cross sections exhibited, for small collision energies, Stueckelberg oscillations, which were due to interference of scattering on the attractive A²Π potential and the repulsive B²Σ potential. For higher collision energies, these oscillations were missing at large angles. With the A²Π potential known from other sources, the repulsive B²Σ potential can be detd. A shoulder in this repulsive potential was responsible for the absence of the interference oscillations at higher scattering energies.