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Cross-talk limits of monolithic highly-segmented semiconductor detectors for high-resolution X-gamma spectrometry are investigated. Cross-talk causes false signal components yielding amplitude losses and fold-dependent shifts of the spectral lines, which partially spoil the spectroscopic performance of the detector. Two complementary electrical models are developed, which describe quantitatively the inter-channel cross-talk of monolithic segmented detectors whose electrodes are read out by charge-sensitive preamplifiers. The first is here designated as Cross-Capacitance (CC) model, the second as Split-Charge (SC) model. The CC model builds around the parasitic capacitances Cij linking the preamplifier outputs and the neighbor channel inputs. The SC model builds around the finite-value of the decoupling capacitance CC used to read out the high-voltage detector electrode. The key parameters of the models are individuated and ideas are shown to minimize their impact. Using a quasi-coaxial germanium segmented detector it is found that the SC cross-talk becomes negligible for decoupling capacitances larger than 1 nF, where instead the CC cross-talk tends to dominate. The residual cross-talk may be reduced by minimization of stray capacitances Cij, through a careful design of the layout of the Printed Circuit Board (PCB) where the input transistors are mounted. Cij can be made as low as ~5 fF, but it is shown that even in such case the impact of the CC cross-talk on the detector performance is not negligible. Finally, an algorithm for cross-talk correction is presented and elaborated.