The pilot was landing his homebuilt, tailwheel-equipped airplane at a private, 2,000 foot long gravel-covered runway. He said that during the landing roll, the airplane veered slightly to the left, and he applied right rudder to correct the veer. As he depressed the right rudder pedal, the airplane's tail began to rise, and the airplane subsequently nosed over, sustaining substantial damage to the wings and fuselage. The pilot noted that there were no preaccident mechanical anomalies with the airplane.