It is evident that there is no uniform method of calculating meteor radiants which would yield reliable resilts for all types of cometary orbits. In the present paper an analysis of this problem is presented, together with recommended methods for various types of orbits. Some additional methods resulting from mathematical modelling are presented and discussed together with Porter's, Steel-Baggaley's and Hasegawa's methods. In order to be able to compare how suitable the application of the individual radiant determination methods is, it is necessary to determine the accuracy with which they approximate real meteor orbits. To verify the accuracy with which the orbit of a meteoroid with at least one node at 1 AU fits the orignal orbit of the parent body, we applied the Southworth-Hawkins D-criterion (Southworth and Hawkins, Smithson Contr. Astrophys.7, 261, 1963). D ⩽ 0.1 indicates a very good fit of orbits, 0.1 < D ⩽ 0.2 is considered to be a good fit of orbits, and D > 0.2 the fit is rather poor and the change of orbit unrealistic. The optimal methods with the smallest values of D for given types of orbits anre shown in three plots. The new mathod of retation around the line of apsides we propose is very appropriate is the region of small inclinations Hasegawa's ω-adjustment method ( Publ. Astrpn. Soc. Jpn42, 175, 1990) has the widest application.