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In this paper, we investigate multi-user modular extremely large-scale multiple-input multiple-output (XL-MIMO) communication systems, where modular extremely large-scale uniform linear array (XL-ULA) is deployed at the base station (BS) to serve multiple single-antenna users. By exploiting the unique modular array architecture and considering the potential near-field propagation, we develop sub-array based uniform spherical wave (USW) models for distinct versus common angles of arrival/departure (AoAs/AoDs) with respect to different sub-arrays/modules, respectively. Under such USW models, we analyze the beam focusing patterns at the near-field observation location by using near-field beamforming. The analysis reveals that compared to the conventional XL-MIMO with collocated antenna elements, modular XL-MIMO can provide better spatial resolution by benefiting from its larger array aperture. However, it also incurs undesired grating lobes due to the large inter-module separation. Moreover, it is found that for multi-user modular XL-MIMO communications, the achievable signal-to-interference-plus-noise ratio (SINR) for users may be degraded by the grating lobes of the beam focusing pattern. To address this issue, an efficient user grouping method is proposed for multi-user transmission scheduling, so that users located within the grating lobes of each other are not allocated to the same time-frequency resource block (RB) for their communications. Numerical results are presented to verify the effectiveness of the proposed user grouping method, as well as the superior performance of modular XL-MIMO over its collocated counterpart with densely distributed users.