The problem of emittance growth due to random fluctuations of the magnetic field in a hadron collider is considered. It is shown that the transverse feedback system can suppress strongly the emittance growth. The main effect limiting a suppression degree is the betatron tube spread due to head‐on beam‐beam effects. A simple analytical model is considered. Its results are in a good coincidence with computer simulations. The dependencies of the emittance growth rate on noise spectral density, beam separation at the Interaction Point (IP), and value of beam separation at long‐range collisions are studied. The results are applicable to the Superconducting Super Collider. © 1995American Institute of Physics