Hamsi is one of 14 remaining candidates in NIST's Hash Competition for the future hash standard SHA-3. Until now, little analysis has been published on its resistance to differential cryptanalysis, the main technique used to attack hash functions. We present a study of Hamsi's resistance to differential and higher-order differential cryptanalysis, with focus on the 256-bit version of Hamsi. Our main results are efficient distinguishers and nearcollisions for its full (3-round) compression function, and distinguishers for its full (6-round) finalization function, indicating that Hamsi's building blocks do not behave ideally.