The triplet {ital nf} Rydberg states of HD with {ital n}=9--17, {ital L}=3, {ital v}=1, and {ital R}=1,3 have been observed and identified with the laser--molecular-beam method. A 20-eV electron beam excites a collimated HD beam to the metastable 2{ital p} {sup 3}{Pi} state. Two counterpropagating cw single-frequency laser beams excite the metastable molecule first to the intermediate 3{ital d} {sup 3}{Pi} state, then to a triplet {ital nf} Rydberg state. The transition frequencies between the 3{ital d} and {ital nf} states have been measured to an accuracy of 0.02 cm{sup {minus}1}. The long-range model gives the transition frequencies to an accuracy of approximately 0.1 cm{sup {minus}1}. Using these energy-level measurements, the ionization potential of the metastable state has been determined to be 27 460.98(30) cm{sup {minus}1} and the energy difference between the triplet metastable and the singlet ground state has been determined to be 97 105.50(30) cm{sup {minus}1}. In addition, the linewidths of the triplet Rydberg states have been measured, giving the autoionization rates.