We present HI 21cm line observations, obtained with the Australia Telescope Compact Array, of two dwarf elliptical galaxies (dEs) in the Fornax cluster: FCC032 and FCC336. The optical positions and velocities of these galaxies place them well within the Fornax cluster. FCC032 was detected at the 3sigma significance level with a total HI flux density of 0.66+-0.22 Jy km s^-1 or an HI mass of 5.0+-1.7 10^7 h_75^-2 M_sun. Based on our deep Halpha+[NII] narrow-band images, obtained with FORS2 mounted on the VLT, this dE was already known to contain 600-1800 h_75^-2 M_sun of ionised Hydrogen (depending on the relative strengths of the Halpha and [NII] emission lines). Hence, this is the first study of the complex, multi-phase interstellar medium of a dE outside the Local Group. FCC336 was detected at the same significance level: 0.37+-0.10 Jy km s^-1 or a total HI mass of 2.8+-0.7 10^7 h_75^-2,M_sun. Using a compilation of HI data of dwarf galaxies, we find that the observed high HI-mass boundary of the distribution of dIrrs, BCDs, and dEs in a log(L_B) versus log (M_HI) diagram is in good agreement with a simple chemical evolution model with continuous star formation. The existence of many gas-poor dEs (undetected at 21cm) suggest that the environment (or more particularly, a galaxys orbit within a cluster) also plays a crucial role in determining the amount of gas in present-day dEs. E.g., FCC032 and FCC336 are located in the sparsely populated outskirts of the Fornax cluster. This is in agreement with HI surveys of dEs in the Virgo Cluster and an Halpha survey of the Fornax Cluster, which also tend to place gas-rich dwarf galaxies in the cluster periphery.
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