have exactly zero electrical resistance - a steady current within a perfect conductor will flow without losing energy to resistance. Resistance is what causes heating in conductors, thus a perfect conductor will generate no heat. Since energy is not being lost to heat, the current will not dissipate; it will flow indefinitely within the perfect conductor until acted upon by an external force.
require a constant magnetic flux - the magnetic flux within the perfect conductor must be constant with time. Any external field applied to a perfect conductor will have no effect on its internal field configuration.