  A new type of hidden order in many body systems is explored. This order
appears in states which are analogues to charge density waves, or spin density
waves, but involve anomalous particle-hole correlations that are odd in
relative time and frequency. These states are shown to be inherently different
from the usual states of density waves. We discuss two methods to
experimentally observe the new type of pairing where a clear distinction
between odd and even correlations can be detected: (i) by measuring the
density-density correlation, both in time and space and (ii) via the
conductivity which, according to the Kubo formula, is given by the
current-current correlation. An order parameter for these states is defined and
calculated for a simple model, illuminating the physical nature of this order.
