The design goal for the TESLA Test Facility Linac is an accelerating gradient of 15 MV/m at a quality factor of Q = 3.10(9). In the linac the cavities are operated in pulsed mode (constant gradient for 800 mu s with 10 Hz repetition rate). The majority of the first 17 industrially produced cavities exceeded the specification. Several cavities reached 25 MV/m at Q > 1.10(10). Due to cleaning by high pressure water rinsing most of the cavities showed no held emission loading; the major limitation was thermal instability. In cavities with poorer performance, two types of held limitations were identified by temperature mapping and further surface analysis: tantalum impurity in the bulk niobium and defects in the equator welds. Eight cavities, equipped with main power coupler, HOM couplers and tuning system have been successfully tested in a horizontal cryostat in pulsed mode. Also here the majority of the cavities exceeded the design goal and gradients up to 25 MV/m could be achieved.