We have calculated the two-point correlation functions in redshift space, xi(sigma,pi), for galaxies of different spectral types in the 2dF Galaxy Redshift Survey. Using these correlation functions we are able to estimate values of the linear redshift-space distortion parameter, beta = Omega_m^0.6/b, the pairwise velocity dispersion, a, and the real-space correlation function, xi(r), for galaxies with both relatively low star-formation rates (for which the present rate of star formation is less than 10% of its past averaged value) and galaxies with higher current star-formation activity. At small separations, the real-space clustering of passive galaxies is very much stronger than that of the more actively star-forming galaxies; the correlation-function slopes are respectively 1.93 and 1.50, and the relative bias between the two classes is a declining function of radius. On scales larger than 10 h^-1 Mpc there is evidence that the relative bias tends to a constant, b(passive)/b(active) ~ 1. This result is consistent with the similar degrees of redshift-space distortions seen in the correlation functions of the two classes -- the contours of xi(sigma,pi) require beta(active)=0.49+/-0.13, and beta(passive)=0.48+/-0.14. The pairwise velocity dispersion is highly correlated with beta. However, despite this a significant difference is seen between the two classes. Over the range 8-20 h^-1 Mpc, the pairwise velocity dispersion has mean values 416+/-76 km/s and 612+/-92 km/s for the active and passive galaxy samples respectively. This is consistent with the expectation from morphological segregation, in which passively evolving galaxies preferentially inhabit the cores of high-mass virialised regions.