Spherical (23) or cylindrical (27, 36) electrodeless ultraviolet lamps are used to remediate fluid, directly or by excitation of ultraviolet-activated photocatalyst surfaces, which may be on the lamps themselves, or on structures which are permeable by the fluid. The lamps may be excited in cavities (18, 19; 43) by microwave energy from a magnetron (22), or by radio frequency power (39) inductively coupled (40) to the lamps. The lamps (44) may have start-up electrodes (47).