  It is shown that the dephasing rate in Coulomb coupled mesoscopic structures
is determined by charge relaxation resistances. The charge relaxation
resistance together with the capacitance determines the RC-time of the
mesoscopic structure and at small frequencies determines the voltage
fluctuation spectrum. Self-consistent expressions are presented which give the
charge relaxation resistance and consequently the dephasing rate in terms of
the diagonal and off-diagonal elements of a generalized Wigner-Smith delay-time
matrix. Dephasing rates are discussed both for the equilibrium state and in the
transport state in which charge fluctuations are generated by shot noise. A
number of different geometries are discussed. This article is to appear in {\it
Quantum Mesoscopic Phenomena and Mesoscopic Devices}, edited by I. O. Kulik and
R. Ellialtioglu, (Kluwer, unpublished).
