The absolute disintegration rate of sources of radioisotopes that decay by electron capture is determined by the X-gamma ray coincidence counting method. The counting system consists of an X-ray and a gamma-ray detector, two single channel pulse height analyzers, a fast-slow coincidence circuit and three scalers. The detectors are of scintillation type with a NaI crystal; the crystal for the gamma-ray detector is 13/4"φ×2" and that for the X-ray detector is 2 mm thick to minimize the background effect caused by energetic gamma-rays, this effect being measured by inserting a copper plate of 0.5 mm thick as an X-ray filter between the detector and the source. An A-1 type low noise preamplifier with a gain of 25 is used to amplify output signals from the X-ray detector. The X-rays and the gamma-rays, which are to be coincided, are selected by the respective pulse height analyzers. The resolving times of the fast and slow coincidence circuits. are 2 and 6 μsec. respectively. The normality of operation of the system is examined by the absolute measurement of disintegration rate of a ⁸⁸Y source, the characteristic X-rays and 1.83 MeV gamma-rays emitted from ⁸⁸Y are coincided. The absolute disintegration rate of this source is. also measured by the gamma-ray scintillation spectrometrical method with a 3"φ×3" NaI crystal scintillation detector and a TMC 256 channel pulse height analyzer. The photopeak efficiency of this spectrometer is determined by the use of ¹³⁷Cs, ⁶⁰Co and ²⁴Na sources, the absolute disintegration rates of which are determined in advance by the 4πβ counting or 4πβ-γ coincidence method. The disintegration rate of ⁹⁹Y sources obtained by the X-gamma ray coincidence method is in good agreement with that obtained by the scintillation spectrometrical method.