This thesis investigates the stem concept within inferential-realisational morphology, espe- cially paradigm function morphology (PFM; Stump 2001b), a stem and paradigm (Sp) model (Blevins 2003: 742). The base of a word in a paradigm cell is a stem. The distribution of stems may not coincide with morphosyntactic property values, so it is not possible to suc- cessfully associate meaning to stems: stems are morphomic. Stems may also be the base of another stem, which is therefore complex. Each paradigm cell contains a morphome, which maps a lexeme to i phonetic strings, where i >0, realising the cell's morphosyntactic properties (Aronoff 1994). One theory based on the morphomic stem is PFM. However, whereas PFM is fully able to form simple morphomic stems, some reformulation is required to enable complex morphomic stem formation. The aim of this thesis is to perform that reformulation. To test the reformulation, data with complex stems were required, entailing that the data be segmented into stem plus affixes. No consistent procedure existed, so a procedure was devised, based on the distribution of phonetic substrings throughout each system. The strictly morphomic stem hypothesis (Spencer 2012) was used to assign components as stem or affix. The stem rules of PFM were replaced by a stem formation function (SF), a morphomic analogue of the paradigm function: the morphomic index replaces the morphosyntactic property index. The SF is invoked upon stem selection. If the stem is simple, the morphomic analogue of stem selection rules selects the stem base; subsequent rule blocks do nothing. If the stem is complex, the first block selects a stem and the subsequent blocks add further phonetic material. The PF was changed to input and output an array of phonetic strings rather than single strings to allow PFM to model all values of i. Paradigm function morphology was easily modified to accommodate morphomic stems of any complexity. This, together with permitting multiple phonetic strings to be output, makes PFM a flexible, powerful framework with which to perform morphological analysis.