  In a recent publication we have calculated elastic charmonium production in
ep collisions employing realistic charmonia wave functions and dipole cross
sections and have found good agreement with the data in a wide range of s and
Q^2. Using the ingredients from those calculations we calculate exclusive
electroproduction of charmonia off nuclei. Here new effects become important,
(i) color filtering of the c-cbar pair on its trajectory through nuclear
matter, (ii) dependence on the finite lifetime of the c-cbar fluctuation
(coherence length) and (iii) gluon shadowing in a nucleus compared to the one
in a nucleon. Total coherent and incoherent cross sections for C, Cu and Pb as
functions of s and Q^2 are presented together with some differential cross
sections. The results can be tested with future electron-nucleus colliders or
in peripheral collisions of ultrarelativistic heavy ions.
