Millimeter-wave transitions between high-n Rydberg states of several isotopes of xenon have been recorded at sub-megahertz resolution. The fine and, for 129 Xe and 131 Xe, hyperfine structures of s, p, d, and f Rydberg states with principal quantum number in the range 52 n 64 have been determined from combination differences and analyzed using multichannel quantum defect theory. Improved eigenquantum defects and channel interaction parameters for the odd-and even-parity Rydberg states of xenon and the hyperfine structure of the 2 P 3/2 ground state of 129 Xe + and 131 Xe + have been obtained. Nearly degenerate p and d fine or hyperfine levels are very easily mixed by even weak stray electric fields.