  We present ASCA observations of the nearby galaxies Dwingeloo 1 (Dw1) and
Maffei 1 (Mf1). X-ray sources are clearly detected within 3 arcminutes of the
optical nuclei of both galaxies. Despite the low Galactic latitude of these
fields ($|b|<1\degmark$) we conclude, on probability and spectral grounds, that
the detected sources are intrinsic to these galaxies rather than foreground or
background interlopers. The Dw1 source, designated Dw1-X1, is interpreted as
being either a hyper-luminous X-ray binary (with a 0.5--10\,keV luminosity of
more than $10^{39}\ergps$) or an X-ray bright supernova. The Mf1 emission is
hard and extended, suggesting that it originates from a population of X-ray
binaries. Prompted by the Dw1-X1 results, we discuss the nature of
hyper-luminous X-ray binary systems. Such sources are commonly seen in nearby
galaxies with a frequency of approximately one per galaxy. We present a
possible connection between these luminous systems and Galactic superluminal
sources.
