Massive central stars (M > 1 Mo) of planetary nebulae burn nuclear fuel on a time scale of hundreds or tens of years which is shorter than the recombination time in a typical planetary nebula. Consequently the ionization and thermal structure of a nebula with such a nucleus is expected to be far from equilibrium conditions. The greatest chance of observing such a nebula is when the central star cools down to the white dwarf region. Time-dependent photoionization models suggest the following non-equilibrium effects to be expected at this stage. Firstly, the nebula shows a double shell structure, i.e. a bright, inner ring is surrounded by a faint, extended halo best seen in the HI lines and infrared lines from low-ionization species, such as (Ne II) 12.8 μ. Secondly, the low-excitation emission ((O II), (Ne II), (S III)) is enhanced relative to the high-excitation ((O III), (Ne III), (S III)). Thirdly, different modifications of the Zanstra method result in significantly different temperatures for the central star with a general rule that THI > THeII > THeII/HI The He II Zanstra method gives the most reliable result. Fourthly, the electron temperature derived from the (O III) lines is appreciably higher than that obtained from the (N II) lines. It is suggested that NGC 7027 and NGC 2440 possess massive central stars and that the above time-dependent effects are currently observed in these nebulae.