The behavior of the nucleon electromagnetic form factors in infinite nuclea
r matter has been investigated on the basis of a chiral- and scale-invarian
t effective Lagrangian. With increasing matter density, the nucleon form fa
ctors decrease, while the root-mean-square nucleon radii increase with resp
ect to their vacuum values. By way of example, we indicate that, at a norma
l nuclear density and a squared momentum transfer of q(2) = 7.5 fm(-2), the
proton and neutron electric form factors decrease by 17 and 4%, respective
ly.