Abstract. On the basis of the relative line intensity ratio (RLIR) method, transition probability values of the spontaneous emission (Einstein's A values) of 14 transitions in the singly (Kr II) and 7 transitions in doubly (Kr III) ionized krypton spectra have been obtained relatively to the reference A values related to the 435.548 nm Kr II and 324.569 nm Kr III, the most intensive transitions in the Kr II and Kr III spectra. Our Kr III transition probability values are the first data obtained experimentally using the RLIR method. A linear, low-pressure, pulsed arc operated in krypton discharge was used as an optically thin plasma source at a 17 000 K electron temperature and 1.65 × 10 23 m −3 electron density. Our experimental relative A values are compared with previous experimental and theoretical data.