  We present comprehensive multiwavelength observations of three gamma-ray
bursts (GRBs) with durations of several thousand seconds. We demonstrate that
these events are extragalactic transients; in particular we resolve the
long-standing conundrum of the distance of GRB 101225A (the "Christmas-day
burst"), finding it to have a redshift z=0.847, and showing that two apparently
similar events (GRB 111209A and GRB 121027A) lie at z=0.677 and z=1.773
respectively. The systems show extremely unusual X-ray and optical lightcurves,
very different from classical GRBs, with long lasting highly variable X-ray
emission and optical light curves that exhibit little correlation with the
behaviour seen in the X-ray. Their host galaxies are faint, compact, and highly
star forming dwarf galaxies, typical of "blue compact galaxies". We propose
that these bursts are the prototypes of a hitherto largely unrecognized
population of ultra-long GRBs, that while observationally difficult to detect
may be astrophysically relatively common. The long durations may naturally be
explained by the engine driven explosions of stars of much larger radii than
normally considered for GRB progenitors which are thought to have compact
Wolf-Rayet progenitor stars. However, we cannot unambiguously identify
supernova signatures within their light curves or spectra. We also consider the
alternative possibility that they arise from the tidal disruption of stars by
supermassive black holes.
