  We investigate the influence of critical spin fluctuations on electromagnetic
responses in the odd-frequency superconductivity. It is shown that the Meissner
kernel of the odd-frequency superconductivity is strongly reduced by the
critical spin fluctuation or the massless spin wave mode in the
antiferromagnetic phase. These results imply that the superfluid density is
reduced, and the London penetration depth is lengthened for the odd-frequency
pairing. It is also shown that the zero field Flude-Ferrell-Larkin-Ovchinnikov
pairing is spontaneously realized both for even- and odd-frequency in the case
of sufficiently strong coupling with low lying spin-modes.
