  Extension of the braid relations to the multiple braided tensor product of
algebras that can be used for quantization of nonultralocal models is
presented. The Yang--Baxter--type consistency conditions as well as conditions
for the existence of the multiple coproduct (monodromy matrix), which can be
used for construction of the commuting subalgebra, are given. Homogeneous and
local algebras are introduced, and simplification of the Yang--Baxter--type
conditions for them is shown. The Yang--Baxter--type equations and multiple
coproduct conditions for homogeneous and local of order 2 algebras are solved.
