Kinetic parameters of macromolecular systems are important for their function in vitro and in vivo. These parameters describe how fast the system dissociates (the characteristic dissociation time), and how fast the system reaches equilibrium (characteristic relaxation time). For many macromolecular systems, the transitions within the systems are described as a random walk through a number of states with various free energies. The rate of transition between two given states within the system is characterized by the average time which passes between starting the movement from one state, and reaching the other state. This time is referred to as the mean first-passage time between two given states. The characteristic dissociation and relaxation times of the system depend on the first-passages times between the states within the system. Here, for a one-dimensional random walk we derived an equation, which connects the mean first-passage time between two states with the free energies of the states within the system. We also derived the general equation, which is not restricted to one-dimensional systems, connecting the relaxation time of the system with the first-passage times between states. The application of these equations to DNA branch migration, DNA structural transitions and other processes is discussed.