A Brownian dynamics treatment in torsional angle space is presented for the simulation of conformational dynamics of macromolecules with fixed bond lengths and band angles and with an arbitrary intramolecular potential energy function. The advantages of the torsional angle space treatment over similar treatments (Brownian dynamics or molecular dynamics) in atomic coordinate space are that, first, the number of variables is reduced by roughly a factor of 10 and, second, the integration time step size is increased by 3 to 4 orders of magnitude (because, by confining the treatment to the torsional angle space, the time step size is not limited by the fast oscillation modes of covalent bonds but rather by the slow motion of macromolecular segments whose time scale is roughly 3 to 4 orders of magnitude larger than that of bond oscillations). Consequently, the exploration of global conformational relaxation processes becomes computationally possible. The treatment is tested by studying the folding kinetics of off-lattice chains with fixed bond lengths and bond angles and with prescribed sequences. The present treatment is a general purpose one applicable to all macromolecular conformational relaxation processes (e.g., protein folding kinetics, drug/ligand docking on to target proteins, conformational multiple-minima problems, etc.). It serves as a complement to the molecular dynamics or Brownian dynamics treatments in atomic coordinate space.