A significant number of cataclysmic variables were detected as hard X-ray sources in the INTEGRAL survey, most of them of the magnetic intermediate polar type. We present a detailed X-ray broad-band study of two new sources, IGR J00234+6141 and 1RXS J213344.1+510725, that allow us to classify them as secure members of the intermediate polar class. Timing and spectral analysis of IGR J00234+6141 are based on a XMM-Newton observation and INTEGRAL publicly available data. For 1RXS J213344.1+510725 we use XMM-Newton and Suzaku observations at different epochs, as well as INTEGRAL publicly available data. We determine a spin period of 561.64 +/- 0.56 s for the white dwarf in IGR J00234+6141. The X-ray pulses are observed up to about 2 keV. From XMM-Newton and Suzaku observations of 1RXS J213344.1+510725, we find a rotational period of 570.862 +/- 0.034 s. The observations span three epochs where the pulsation is observed to change at different energies both in amplitude and shape. In both objects, the spectral analysis spanned over a wide energy range, from 0.3 to 100 keV, shows the presence of multiple emission components absorbed by dense material. The X-ray spectrum of IGR J00234+6141 is consistent with a multi-temperature plasma with a maximum temperature of about 50 keV. In 1RXS J213344.1+510725, multiple optically thin components are inferred, as well as an optically thick (blackbody) soft X-ray emission with a temperature of about 100 eV. This latter adds 1RXS J213344.1+510725 to the growing group of soft X-ray intermediate polars. (abridged)
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