The possibility of singularities arising in Burgers' equation is discu
ssed and some arguments are put forward in favour of the suggestion th
at non-singular initial conditions cannot produce the singularity in t
he process of time evolution in real time. However, consideration of c
omplex time supplies us with examples of the appearance of singulariti
es. The broad class of exactly integrable initial conditions for Burge
rs' equation is presented. (C) 1997 Elsevier Science B.V.