  We define a group of extended non-Abelian gauge transformations for tensor
gauge fields. On this group one can define generalized field strength tensors,
which are transforming homogeneously with respect to the extended gauge
transformations. The generalized field strength tensors allow to construct two
infinite series of gauge invariant quadratic forms. Each term of these infinite
series is separately gauge invariant. The invariant Lagrangian is a linear sum
of these forms and describes interaction of tensor gauge fields of arbitrarily
large integer spins 1,2,.... It does not contain higher derivatives of the
tensor gauge fields, and all interactions take place through three- and
four-particle exchanges with dimensionless coupling constant. The first term in
this sum is the Yang-Mills Lagrangian.
  The invariance with respect to the extended gauge transformations does not
fix the coefficients - the coupling constants - in front of these forms. There
is a freedom to vary them without breaking the extended gauge symmetry. We
demonstrate that by an appropriate tuning of these coupling constants one can
achieve an enhancement of the extended gauge symmetry. This leads to highly
symmetric equations. We present the explicit form of the free equations for the
rank-2 and rank-3 gauge fields. Their relation to the Schwinger free equation
for the rank-3 gauge fields is discussed.
