  This paper describes the calculation of the electromagnetic form factor of
the K0 meson at order p^6 of chiral perturbation theory which is the
next-to-leading order correction to the well-known p^4 result achieved by
Gasser and Leutwyler. On the one hand, at order p^6 the chiral expansion
contains 1- and 2-loop diagrams which are discussed in detail. Especially, a
numerical procedure for calculating the irreducible 2-loop graphs of the sunset
topology is presented. On the other hand, the chiral Lagrangian L^6 produces a
direct coupling of the K0 current with the electromagnetic field tensor. Due to
this coupling one of the unknown parameters of L^6 occurs in the contribution
to the K0 charge radius.
