"The for scalar electrodynamics in Fermi gauges are shown to imply a homogeneous first-order partial differential equation for the effective potential involving only the gauge parameter and the external scalar field. Spontaneous symmetry breaking is consequently a gauge-invariant phenomenon. Also observable quantities, including masses, physical coupling constants, and elements, of a theory with spontaneous symmetry breaking are found to be invariant, if a change in the gauge parameter is accompanied by a suitable change in the ground-state expectation value of the scalar field. The generalization to a non-Abelian gauge theory is briefly indicated."