Monitoring the HRI onboard ROSAT failed to detect the nearby faint M dwarf star Gl 105B (a star of anornalously low chromospheric and coronal activity), implying log L_{x} < 26.1. High resolution optical data for CaII HK indicate a surface flux of ~ 6.5 10^{3} erg cm^{-2} s^{-1}, in good agreement with the previously measured Mg II hk flux. Based on chromospheric modelling both the H alpha and CaII K line profiles indicate an atmospheric structure which is intermediate between that of an intermediate dM chromospehre and a basal chromosphere. Also, the modelling indicates that a better fit is obtained using a model atmosphere which has T_{min} less than 2650 K, and a thin steep chromosphere. Furthermore, the CaII HK radiative losses may only be ~5% of the radiative losses in the UV continuum, implying total chromospehric losses in excess of 10^{5} erg cm^{-2} s^{-1}.