Asteroids in cometary orbits can be defined as minor planets that do not present cometary activity and has orbits with Tisserand parameter T < 3 (typical of cometary orbits). The nature and origin of this population is still controversial. Recent dynamical studies claim for a cometary origin (comets that become dormant or dead comets by the growth of an insulating surface crust of refractory material) or an asteroidal origin (asteroids of the outer main belt whith orbits that become cometary because of dynamical reasons). In an effort to determine the nature of this objects we started an observational program of a set of these asteroids with the aim of characterize some physical properties of the population and to compare them with that of outer main belt asteroids and cometary nuclei. In particular, NEAs in cometary orbits are very important to determine the number of dead comets in the NEA population and because they are good targets for space missions. In this work a preliminary analysis of our database of visible+infrared spectra (0.5-2.4 μm), that includes more than 20 objects observed with the Italian 3.56m "Telescopio Nazionale Galileo" and the 2.5m "Nordic Optical Telescope" at the "El Roque de los Muchachos" Observatory (La Palma, Spain), is presented. The spectral characteristics and the main mineralogical properties of their surfaces is discussed in comparison with that of Trojan, Hilda asteroids and cometary nuclei. Also the spin properties are studied and preliminary results of our photometric program using the 1m "Optical Ground Station" and the 0.82m "IAC-80" telescopes at Teide Observatory (Tenerife, Spain) are presented. Finally the size distribution is also studied based in their absolute magnitudes.