The AES-256 has received less attention in cryptanalysis than the 192 or 128-bit versions of the AES. In this paper we propose new attacks on 9 and 10-round AES-256. In particular we present a 9-round attack on AES-256 which has the lowest data complexity of all known 9-round attacks. Also, our 10-round attack has a lower data complexity than all known attacks on AES-256. Also, our attack is the first that uses a key differential with probability below one in combination with a related-key boomerang attack. This leads to better related-key differentials which contain less non-zero byte differences and rounds with zero byte differences in each byte of a subkey difference.