  We define a monoidal semantics for algebraic theories. The basis for the
definition is provided by the analysis of the structural rules in the term
calculus of algebraic languages. Models are described both explicitly, in a
form that generalises the usual definition in sets; and from a
category-theoretical point of view, as monoidal functors on suitable
classifying categories. The semantics obtained includes as special cases both
the semantics of ordinary algebraic theories in Cartesian categories, and the
semantics of operads and multicategories over sets.
