Transport properties of antiferromagnetic superconductors with T(N) < T(c) have been investigated. Detailed numerical results are given for SmRh4B4 by using the following model. The paramagnetic phase (T(N) < T < T(c)) is described by using Abrikosov-Gorkov theory of magnetic ions in an ordinary superconductor. In the AF phase (T less-than-or-equal-to T(N)), the effects of the molecular field H(Q)(T) and the elastic scattering of conduction electrons from spin fluctuations are included. Expressions for H(Q)(T) and the scattering rate from spin fluctuations have been derived. The aim has been to see if properties are enhanced or depressed by the AF ordering occurring below T(N). It is found that whereas the electronic thermal conductivity K(s), nuclear spin relaxation rate R(s), and the longitudinal ultrasonic attenuation alpha(s), are depressed by the AF ordering, the inverse of the magnetic penetration depth, [lambda(T)]-1, is enhanced below T(N). The effect of all types of impurities is included in the study. Theoretical results for K(s) and [lambda(T)]-1 agree with the experimental values for SmRh4B4 (experimental data for other properties are not available in literature). In the above, T(N) is the Neel temperature and T(c) is superconducting transition temperature.