The pilot flying balloon N2037U stated that he was making an approach to land when he noticed balloon N20513 behind him making an approach as well. He heard the envelope of his balloon tearing and observed the basket of N20513 ripping the material. The pilot opened both burners and instructed the passengers to brace themselves during touchdown. N2037U contacted the ground and bounced, momentarily becoming airborne again before touching down. The pilot flying balloon N20513 stated that he was making an approach to land and observed balloon N2037U landing ahead of his position. He noticed N2037U began to slow as it was descending through about 10 feet above ground level. He realized that the balloons' envelopes may touch, which he noted was not uncommon during takeoffs and landings. As N2037U came closer into his view, he thought the contact may push it into the ground and decided to ascend. During the climb, the basket of his balloon collided with the envelope of N2037U, tearing two of its panels. He landed his balloon without further incident. The pilot of N20513 stated that the accident may have been prevented if he had maintained the same altitude as N2037U. Both pilots stated that there were no preimpact mechanical malfunctions or failures with the balloons that would have precluded normal operation.