  The nucleon strange vector and isoscalar electromagnetic form factors are
studied using a spectral decomposition. The K\bar{K} contribution to the
electric and magnetic radii as well as the magnetic moment is evaluated to all
orders in the strong interaction using an analytic continuation of experimental
KN scattering amplitudes and bounds from unitarity. The relationship between
non-resonant and resonant K\bar{K} contributions to the form factors is
demonstrated, and values for the vector and tensor \phi N\bar{N} couplings are
derived. The K\bar{K} spectral functions are used to evaluate the credibility
of model calculations for the strange quark vector current form factors.
