In the paper are defined the following concepts: syntax-directed translation scheme (SDTS), form of SDTS, rule of SDTS, syntax-directed translation (SDT), input grammar of SDTS, input language of SDTS, output grammar of SDTS, output language of SDTS, bi-unique SDT, conditions of composition of SDTs, conditions of equality of SDTs, identical SDT, inverse SDT, simple SDTS, simple SDT and compound SDT, and are proved 13 theorems about some properties (equivalence, composition, commutation, association and unity) of SDTs.