A tagmeme is the smallest functional element in the grammatical structure of a language. The term was introduced in the 1930s by the linguist Leonard Bloomfield, who defined it as the smallest meaningful unit of grammatical form (analogous to the morpheme, defined as the smallest meaningful unit of lexical form). The term was later adopted, and its meaning broadened, by Kenneth Pike and others, beginning in the 1950s, who used it as the basis for their tagmemics.
According to the scheme set out by Leonard Bloomfield in his book Language (1933), the tagmeme is the smallest meaningful unit of grammatical form. A tagmeme consists of one or more taxemes, where a taxeme is a primitive grammatical feature, in the same way that a phoneme is a primitive phonological feature. Taxemes and phonemes do not as a rule have meaning on their own, but combine into tagmemes and morphemes respectively, which do carry meaning.
For example, an utterance such as "John runs" exemplifies a tagmeme whose meaning is that an actor performs an action. The taxemes making up this tagmeme include the selection of a nominative expression, the selection of a finite verb expression, and the ordering of the two such that the nominative expression precedes the finite verb expression.