A theoretical approach to the description of longitudinal (T(1)) relaxation in scalar coupled systems of spin 1/2 nuclei at arbitrary magnetic field is developed, which is based on the Redfield theory. The consideration is addressed to field-cycling relaxometry experiments with high-resolution NMR detection, in which the field dependence of T(1)-relaxation times, the nuclear magnetic relaxation dispersion (NMRD), can be studied for individual spins of the molecule. Our study reveals well-pronounced effects of spin-spin couplings on the NMRD curves. First, coupled spins having completely different high-field T(1) times tend to relax at low field with a common relaxation time. Second, the NMRD curves exhibit sharp features at the fields corresponding to the positions of nuclear spin level anticrossings. Such effects of spin-spin couplings show up not only for individual spins but also for the T(1)-relaxation of the total spin magnetization of the molecule. The influence of spin-spin coupling is of importance as long as the coupling strength J is larger than the inverse T(1)-relaxation times of the spins. Around J x T(1) = 1 there is also a coherent contribution to the relaxation kinetics resulting in an oscillatory component of the kinetic curves. Application of the theory to experimental examples will be described in subsequent publications.