The absorption spectrum of the KAr molecule has been observed with high resolution between 13032 and 13077cm −1 using tunable laser diodes as light sources, a supersonic beam for production of the molecules, and laser-induced fluorescence for detection. In addition, optical–optical double resonance (OODR) experiments have been performed to simplify the spectrum and to get rotational assignment. Altogether, 670 lines due to the transition B 2 Σ + ←X 2 Σ + have successfully been assigned with vibrational levels of the B state ranging from v=0 to v=6. The corresponding energy values were fitted to the well-known Dunham expansion. In addition, we were able to analyse a local perturbation between the vibrational level v=1 of the B state and v=14 of the A 2 Π 3/2 state. Unexpected extra lines in the OODR spectra are most probably due to a collision-induced population of other levels. For the equilibrium distance and the well-depth of the B state we obtain from the Dunham expansion 7.03 (8)Å and 26.2 (8)cm −1 , respectively.