  Double logarithms resummation has been much studied in inclusive as well as
exclusive processes. The Sudakov mechanism has often be the crucial tool to
exponentiate potentially large contributions to amplitudes or cross-sections
near phase-space boundaries. We report on a recent work where a very different
pattern emerges : the DVCS quark coefficient function C(x,\xi) develops, near
the particular point x=\xi, a non-alternate series in \alpha_s^n
log^{2n}(x-\xi) which may be resummed in a cosh[K sqrt \alpha_s log(x-\xi)]
factor. This result is at odds with the known result for the corresponding
coefficient function for the pion transition form factor near the end point
C(z) although they are much related through a z -> x/\xi correspondence.
