Previous work suggested that P/Neujmin I and P/Arend-Rigaux may represent a transition phase between comet and minor planet. Earlier results on the librations of minor planets are confirmed here by means of numerical integrations in which allowance is also made for the perturbations by planets other than Jupiter. With the exception of Hidalgo, all known minor planets are able to avoid encounters with Jupiter. Since the short-period comets characteristically have frequent encounters with Jupiter, it follows hat although cometary remnants may look like minor planets, they have subsequent lifetimes that are several orders of magnitude shorter than those of conventional minor planets. A new orbital analysis of Hidalgo sug- gests that nongravitational forces may be acting and that it is an object like P/Neujmin 1 and P/Arend- Rigaux. There is thus little real evidence that comets turn into truly planetary objects, and it is still question- able whether the Apollo objects, for example, can be ex-comets. Long-term analysis shows that short-period comets are sometimes affected by librations similar to those involving minor planets, although the librations are of a temporary nature, existing for a millennium or so, and still often involve close approaches to Jupiter. However, P/Arend-Rigaux and P/Neujmin 1 have apparently been more successful than all other short- period comets in avoiding Jupiter. P/Neujmin 1 is found to librate about the 2 :3 resonance with Jupiter (i.e., in an 18-yr period) in spite of the strong gravitational influence of Saturn. Because its perihelion distance must have remained relatively constant for centuries (or even millennia), it is reasonable that a comet that avoids Jupiter or temporarily librates could indeed be approaching the end of its cometary life.