Relative time dependence as gauge freedom and bilocal models of hadrons

We introduce the shift of relative time variable as a gauge transformation of bilocal field operator. The corresponding gauge invariant free bilocal Lagrangian theory is formulated. The subsidiary condition which eliminates the relative time appears as a gauge invariance condition for bilocal field operator. As an example we quantize the bilocal field describing covariant three dimensional oscillator model of hadrons.