  The new generalization of the gauge interaction for the bosonic strings is
found. We consider some quasiequivariant maps from the space of metrics on the
worldsheet to the space of $n$-tuples of one- and two-dimensional loops. The
two-dimensional case is based on the cylinders interacted with a path space
connection. The special 2-gauge string model is formulated using two
1-connections, non-Abelian background symmetric tensor field and non-Abelian
2-form. The branched non-Abelian space-time is the result of our construction.
