  We introduce the concept of a disjoint partial difference family (DPDF) and
an external partial difference family (EPDF), a natural generalisation of the
much-studied structures of disjoint difference family (DDF), external
difference family (EDF) and partial difference set (PDS). We establish
properties and constructions, and indicate connections to other
recently-studied combinatorial structures. We show how DPDFs and EPDFs may be
formed from collections of PDSs, and also present cyclotomic methods yielding
DPDFs and EPDFs whose component sets are not in general PDSs. As part of this,
we develop a unified framework encompassing various known constructions for
cyclotomic difference structures, which also yields new results on DDFs and
EDFs.
