A linear, nonradial, nonadiabatic pulsation stability analysis of stellar models with effective temperatures 150,000, 155,000, 160,000, and 165,000 K, and luminosities characteristic of stars evolving from AGB to the white dwarf cooling sequence, has been performed. The purpose is to find unstable pulsation modes with periods as long as those observed in the central star of the planetary nebula, K1-16. These models have masses of 0.6 solar masses and homogeneous compositions of half-carbon and half-oxygen by mass. All these stellar models exhibit unstable nonradial modes with periods ranging from 1000 to 4000 s. The longest periods were found in the model with T(e) = 155,000 K, L = 2000 solar luminosities. The pulsation driving mechanism is the cyclical ionization of carbon and oxygen at temperatures of 2-5 million K. This analysis demonstrates that K1-16 is probably a member of the PG 1159-035 class of sdO variable stars. This star is, therefore, an evolutionary link from the central stars of the OVI planetary nebulae to the hottest non-DA white dwarfs as proposed by Sion, Liebert, and Starrfield (1985). It must also be evolving very rapidly.