The NaK 1 (3)Delta state has been studied by the perturbation-facilitated optical-optical double resonance technique. Mixed singlet-triplet levels, A(2)(1)Sigma (+)(upsilon (A),J)similar tob(1)(3)Pi>(*) over bar *(upsilon (b),J), were pumped from thermally populated rovibrational levels of the ground state, X(1)(1)Sigma (+)(upsilon (X),J +/-1), using a single-mode cw dye laser. A single-mode cw Ti:Sapphire laser was then used to further excite the NaK molecules to various 1 (3)Delta>(*) over bar *(upsilon (Delta),N-Delta,J(Delta)) rovibrational levels which were detected by observing collision-induced (3)Lambda -->a(1)(3)Sigma (+) fluorescence in the green part of the spectrum. The measured energies of the 1 (3)Delta>(*) over bar *(upsilon (Delta),N-Delta) levels were fit to a Dunham expansion, and the Dunham coefficients were used to construct the RKR potential curve. Absolute numbering of the 1 (3)Delta state vibrational levels was established by a comparison of experimental and calculated 1 (3)Delta>(*) over bar *(upsilon (Delta),N-Delta,J(Delta))<--b(1)(3)Pi>(*) over bar *(upsilon (b),J(b)) absorption line strengths. A deperturbation program was used to determine the vibration-dependent 1 (3)Delta state spin-orbit interaction parameter. Hyperfine structure of the 1 (3)Delta state was studied, and the Fermi-contact interaction term for this state was determined to be similar to0.0111 cm(-1).