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We investigate the potential for the James Webb Space Telescope (JWST) to detect and characterize the atmospheres of the sub-Neptunian exoplanets in the TOI-270 system. Sub-Neptunes are considered more likely to be water worlds than gas dwarfs. We model their atmospheres using three atmospheric compositions - two examples of hydrogen-dominated atmospheres and a water-dominated atmosphere. We then simulate the infrared transmission spectra of these atmospheres for JWST instrument modes optimized for transit observation of exoplanet atmospheres : NIRISS, NIRSpec and MIRI. We then predict the observability of each exoplanet's atmosphere. TOI-270c and d are excellent targets for detecting atmospheres with JWST transmission spectroscopy, requiring only 1 transit observation with NIRISS, NIRSpec and MIRI; higher signal-to-noise (SNR) can be obtained for a clear H-rich atmosphere. Fewer than 3 transits with NIRISS and NIRSpec may be enough to reveal molecular features. Water-dominated atmospheres require more transits. Water spectral features in water-dominated atmospheres may be detectable with NIRISS in 2 or 3 transits. We find that the detection of spectral features in a cloudy, H-rich atmosphere does not require integrations as long as those required for the water-dominated atmosphere, which is consistent with the differences in atmospheric mean molecular weight. TOI-270c and d could be prime targets for JWST transit observations of sub-Neptune atmospheres. These results provide useful predictions for observers who may propose to use JWST to detect and characterize the TOI-270 planet atmospheres.