  We present Keplerian-type parametrization for the solution of third
post-Newtonian (3PN) accurate equations of motion for two non-spinning compact
objects moving in an eccentric orbit. The orbital elements of the
parametrization are explicitly given in terms of the 3PN accurate conserved
orbital energy and angular momentum in both Arnowitt, Deser, and Misner-type
and harmonic coordinates. Our representation will be required to construct
post-Newtonian accurate `ready to use' search templates for the detection of
gravitational waves from compact binaries in inspiralling eccentric orbits. Due
to the presence of certain 3PN accurate gauge invariant orbital elements, the
parametrization should be useful to analyze the compatibility of general
relativistic numerical simulations involving compact binaries with the
corresponding post-Newtonian descriptions. If required, the present
parametrization will also be needed to compute post-Newtonian corrections to
the currently employed `timing formula' for the radio observations of
relativistic binary pulsars.
