Open-label, non-randomized trial to assess the effectiveness of PXD101 in patients with recurrent or refractory cutaneous or peripheral and other types of T-cell lymphomas. PXD101 is a new, potent histone deacetylase (HDAC) inhibitor. Patients are treated with belinostat(PXD101) 1000 mg/m2 on days 1-5 of a 21 day cycle.