By using gain nonlinearity characteristics of a semiconductor optical amplifier, an all-optical NAND gate at 10 Gbit/s is demonstrated. The all-optical NAND gate operates in single mechanism, which is cross-gain modulation. In the NAND gate (AB~+A~), Boolean AB~ is obtained by using signal A as a probe beam and signal B as a pump beam in SOA-1. Also, Boolean A~ is obtained by using the clock signal as a probe beam and signal A as a pump beam in SOA-2. By adding the two outputs from SOA-1 and SOA-2, Boolean A~+AB~ (logic NAND) can be acquired. The extinction ratio is about 6.1 dB.