We present results for the fourth virial coefficient of quadrupolar Lennard-Jones diatomics for several quadrupole moments and elongations. The coefficients are employed to predict the critical properties from two different truncated virial series. The first one employs the exact second and third virial coefficients, calculated in our previous work. The second includes also the exact fourth virial coefficient as obtained in this work. It is found that the first method yields already fairly good predictions. The second method significantly improves on the first one, however, yielding good results for both the critical temperature and pressure. Particularly, when compared with predictions from perturbation theories available in the literature, the virial series to fourth order compares favorably for the critical temperature. The results suggest that the failure of perturbation theories to predict the critical temperature and pressure is not only related to the neglect of density fluctuations, but also to poor prediction of the virial coefficients. (C) 2003 American Institute of Physics.