It sometimes happens that an object is discovered and thought to be an asteroid and then, at some later time, discovered to show cometary activity. It can also happen that a comet and an asteroid, previously thought to be different objects, are identified through orbital analysis as the same object. The following objects are cross-listed both as a comet and as a minor planet, in order of receiving the dual designation.
(2060) Chiron = 95P/Chiron
This was the first Centaur discovered (1977 UB) and it had an asteroidal appearance upon discovery (C. Kowal in 1977, IAU Circular 3129). Although proposed to be cometary in physical structure shortly after discovery, it was only in the late 1980s that cometary activity was observed, first by anomalous brightening (D. Tholen and collaborators, IAU Circular 4554) and then by directly imaging the coma (K. Meech & M. Belton, IAU Circular 4770).
(4015) Wilson-Harrington = 107P/Wilson-Harrington
This is an example of the second case described above. In 1992 E. Bowell located images of the minor planet (4015) 1979 VA on plates taken in 1949 in the course of the first Palomar Sky Survey. The images had a cometary appearance, rather than the expected asteroidal appearance. B. Marsden then realised that this fuzzy object was comet Wilson-Harrington (1949 III), an object that had been reported in 1949, but that had been poorly followed and was lost. See IAU Circulars 1244, 1248, 1250, 5585, and 5586.
(7968) Elst-Pizarro = 133P/Elst-Pizarro
This is a main-belt object that was discovered by Elst and Pizarro in 1996 and reported by them as a comet with a persistent dust tail (IAU Circular 6456). It was then linked by B. Marsden with a previously known (but not named or numbered) asteroid, 1979 OW7 (IAU Circular 6457).
(60558) Echeclus = 174P/Echeclus
This Centaur was first discovered by Spacewatch in March 2000, reported on MPEC 2000-E64 and MPS 60558, and it was reported as a minor planet in all subsequent reports until Choi and Weissman observed a coma in images taken on 30 Dec 2005. This was followed by numerous other observations of the coma. See MPEC 2000-E64 and IAU Circulars 8656 and 8660 (links not currently available).
(118401) LINEAR = 176P/LINEAR
This is a main-belt asteroid, discovered by Hsieh and Jewitt to have a persistent tail (IAUC 8704 and Science, 23 Mar 2006), much like that of Elst-Pizarro. It seems plausible that this object, Elst-Pizarro above, and P/Read (P/2006 U1) are all members of the Themis family of asteroids as suggested by Hsieh and Jewitt, although the last is just outside the normal definition of the family.
IAU .............. IAU Division III ............. IAU CSBN
Department of Astronomy ............. M. F. A'Hearn ............. The Real World