  We investigate non-linear generalization of Maxwell theory of electromagnetic
field keeping the gauge invariance of Lagrangian. New theory, which is standard
Yang-Mills theory, is based on Harmonic Oscillator HO(4,R) gauge group. It's a
solvable Lie group with nilpotent normal subgroup of codimension 1. We write
down the Yang-Mills equation and point out their pecularities and connection
with standard Maxwell theory.
