  VLBI now has the capability of imaging relatively large fields-of-view (~ 5
arcmin sq) with sub-mJy detection limits. In principle such observations can
distinguish between starburst and AGN activity in cosmologically distant
sources. We present the first deep, wide-field European VLBI Network (EVN) 1.6
GHz observations of faint radio sources in the Hubble Deep Field (HDF) region.
The EVN clearly (> 5sigma) detects 2 radio sources in a field that encompasses
the HDF and part of the Hubble Flanking Fields (HFF). The sources detected are:
VLA J123644+621133 (a z=1.01, low-luminosity FR-I radio source located within
the HDF itself) and VLA J123642+621331 (a dust enshrouded, optically faint,
z=4.424 starburst system). A third radio source, J123646+621404, is detected at
the 4sigma level. The observations presented here, suggest that the radio
emission in the dusty starburst, VLA J123642+621331, arises mainly from AGN
activity, suggesting that in this system, both AGN and starburst activity
co-exist. The prospects for future VLBI deep fields are briefly discussed.
