  We discuss phenomenology of extra time dimensions in a scenario where the
standard model particles are localized in ``our'' time, whereas gravity can
propagate in all time dimensions. For an odd number of extra times, at small
distances, the (real part of the) Newtonian potential is ``screened'' by
tachyonic Kaluza-Klein gravitons. In general, the gravitational self-energy of
objects acquires an imaginary part. This complexity may either be interpreted
as an amplitude for the disappearance into ``nothing'', leading to the
causality and probability violation in low-energy processes, or as an artifact
of the fictitious decay into the unphysical negative energy tachyons. The
former case would put the most severe phenomenological restrictions on such
theories. In the latter case the size of extra times may be within the reach of
the proposed gravitational experiments. In such a case these experiments should
observe that the strength of the Newtonian gravity diminishes at short
distances.
