We apply a recently developed multiterminal formalism to compute the fluctuations in the transport properties of mesoscopic rings. The voltage fluctuations \ensuremath{\delta}V are not symmetric with respect to reversal of the magnetic field H. Contributions to the part of \ensuremath{\delta}V symmetric with respect to reversal of H come from the whole length of the sample, while the antisymmetric part of \ensuremath{\delta}V comes only from the region of the junction between the voltage and current leads. We show that the Aharonov-Bohm (AB) oscillation decreases exponentially with ${C}_{\mathrm{ring}/{L}_{\mathrm{in}}}$ (${C}_{\mathrm{ring}}$ denotes the circumference of the ring, ${L}_{\mathrm{in}}$ denotes the inelastic mean free path). The AB oscillations in the voltage are not symmetric with respect to zero H field---in the highly coherent regime (${C}_{\mathrm{ring}/{L}_{\mathrm{in}<1}}$) the phase of this oscillation can take on any value, while in the classical limit the phase becomes symmetric---0 or \ensuremath{\pi}. We demonstrate the existence of nonlocal voltage fluctuations, ones in which the current path and voltage path do not intersect; both aperiodic fluctuations and AB oscillations fall off exponentially with d/${L}_{\mathrm{in}}$, where d is the closest approach of the current and voltage paths. Finally, we obtain new results on the energy correlation ${E}_{c}$ for the AB effect, finding it to be larger than previously expected.