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The radiative and Auger decay processes of K-shell ionized Np ions are studied theoretically using the flexible atomic code (FAC). Relativistic effects, Breit interaction, QED corrections and nuclear finite mass and volume effects are considered systematically. The resulting calculated K x-rays and Auger spectra of Np are compared with the measured spectra emitted after the electron-capture (EC)-decay of mass-separated 237Pu. The general consistency between theory and experiment is good; the relative intensities and relative positions of the peaks in the measured spectra are reproduced with good accuracy, in spite of the existence of different ways to produce the primary K-shell vacancy, enabling identification of the observed structure in the experimental spectra. We find that most of the radiative transition rates are greater than the Auger transition rates, and the latter decrease rapidly with the transfer of initial vacancies to the outer shell.