  We present a family of model structures on the category of multicomplexes.
There is a cofibrantly generated model structure in which the weak equivalences
are the morphisms inducing an isomorphism at a fixed stage of an associated
spectral sequence. Corresponding model structures are given for truncated
versions of multicomplexes, interpolating between bicomplexes and
multicomplexes. For a fixed stage of the spectral sequence, the model
structures on all these categories are shown to be Quillen equivalent.
