In this paper we introduce the concept of multi-soliton complexes (MSC). A
particular example of a MSC is an incoherent soliton in a multimode fiber o
r in a photorefractive crystal, but there are many examples in other areas
of physics. We discuss a variety of profiles of MSCs, their unusual collisi
onal properties, the possibility of a MSC on a background and some other in
teresting properties of MSCs. Some of their features are also shared by sin
gle solitons, but there are many differences between the properties of the
two types. (C) 2000 American Institute of Physics. [S1054-1500(00)00603-0].