The ESA's X-ray Multi-mirror Mission (XMM-Newton) created a new high-quality version of the XMM-Newton serendipitous source catalogue, 4XMM-DR9, which provides a wealth of information for observed sources. The 4XMM-DR9 catalogue is correlated with the Sloan Digital Sky Survey (SDSS) DR12 photometric data base and the AllWISE data base; we then get X-ray sources with information from the X-ray, optical, and/or infrared bands and obtain the XMM-WISE, XMM-SDSS, and XMM-WISE-SDSS samples. Based on the large spectroscopic surveys of SDSS and the Large Sky Area Multi-object Fiber Spectroscopic Telescope (LAMOST), we cross-match the XMM-WISE-SDSS sample with sources of known spectral classes, and obtain known samples of stars, galaxies, and quasars. The distribution of stars, galaxies, and quasars as well as all spectral classes of stars in 2D parameter space is presented. Various machine-learning methods are applied to different samples from different bands. The better classified results are retained. For the sample from the X-ray band, a rotation-forest classifier performs the best. For the sample from the X-ray and infrared bands, a random-forest algorithm outperforms all other methods. For the samples from the X-ray, optical, and/or infrared bands, the LogitBoost classifier shows its superiority. Thus, all X-ray sources in the 4XMM-DR9 catalogue with different input patterns are classified by their respective models that are created by these best methods. Their membership of and membership probabilities for individual X-ray sources are assigned. The classified result will be of great value for the further research of X-ray sources in greater detail.