We present timing solutions and spin properties of the young pulsar PSR B0540-69 from analysis of 15.8 yr of data from the Rossi X-Ray Timing Explorer. We perform a partially phase-coherent timing analysis in order to mitigate the pronounced effects of timing noise in this pulsar. We also perform fully coherent timing over large subsets of the data set in order to arrive at a more precise solution. In addition to the previously reported first glitch undergone by this pulsar, we find a second glitch, which occurred at MJD 52927 $pm$ 4, with fractional changes in spin frequency $Delta u/ u = (1.64 pm 0.05) times 10^{-9}$ and spin-down rate $Deltadot{ u}/dot{ u} = (0.930 pm 0.011) times 10^{-4}$ (taken from our fully coherent analysis). We measure a braking index that is consistent over the entire data span, with a mean value $n = 2.129 pm 0.012$, from our partially coherent timing analysis. We also investigated the emission behavior of this pulsar, and have found no evidence for significant flux changes, flares, burst-type activity, or pulse profile shape variations. While there is strong evidence for the much-touted similarity of PSR B0540-69 to the Crab pulsar, they nevertheless differ in several aspects, including glitch activity, where PSR B0540-69 can be said to resemble certain other very young pulsars. It seems clear that the specific processes governing the formation, evolution, and interiors of this population of recently born neutron stars can vary significantly, as reflected in their observed properties.
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