To improve knowledge of production rates of nitrogen oxides in turbulent diffusion flames in reaction-sheet regimes, an analytical investigation is made of the structure of a parabolic flamelet. The mixture-fraction field, scalar dissipation rate and gas velocity relative to the flamelet in the vortex are related to flame curvature at the parabolic tip. Flame structure for major species and temperature is described by rate-ratio asymptotics based on two-step and three-step reduced chemical-kinetic mechanisms. Production rates by prompt, thermal and nitrous-oxide mechanisms are obtained from one-step reduced-chemistry approximations that employ steady states for all reaction intermediaries. For sufficiently large streamwise separation distances between isoscalar surfaces, it is found that equilibrium conditions are closely approached near the flame tip, and the thermal mechanism dominates there, but the prompt mechanism always dominates in the wings, away from the tip, where the highest rates of scalar dissipation occur. Increasing the tip curvature increases the Peclet number and the prompt contribution while decreasing the thermal contribution. At 1 atm and ambient temperatures of 300 K, the prompt mechanism always dominates the total production rate in the parabolic flamelet, and, perhaps surprisingly, the rate of the nitrous-oxide mechanism is faster than that of the thermal mechanism and varies with the tip curvature and with scalar dissipation in the same manner as that of the prompt mechanism, different from that of the thermal mechanism. Conclusion reached is that Zel'dovich NO is relatively insignificant in hydrocarbon-air mixtures in reaction-sheet regimes.