Formation and rheological behavior of viscoelastic wormlike micelles in an aqueous solution of a mixed system of nonionic fluorocarbon surfactants, perfluoroalkyl sulfonamide ethoxylate, C8F17SO2N(C3H7)(CH2CH2O)nH (abbreviated as C8F17EOn, n=20 and 3), was studied. A partial ternary phase diagram of water/C8F17EO20/C8F17EO3 was constructed at 25 degrees C by visual inspection through crossed polarizers. In the water/surfactant binary system, C8F17EO20 forms an isotropic micellar solution over a wide concentration range (approximately 80 wt %). The micellar solution of the C8F17EO20 can solubilize a significant amount of C8F17EO3, and the solubility increases with increasing C8F17EO20 concentration. With successive addition of C8F17EO3 to the aqueous C8F17EO20 solution, viscosity increases rapidly, and a viscoelastic solution is formed. The viscosity of the viscous sample was approximately 5th order of magnitude of pure water. The viscoelastic solution follows the Maxwell model typical of wormlike micelles at low-frequency region. With further addition of C8F17EO3 the viscosity decreases, and phase separation occurs. Addition of perfluoropolyether oil, (C3F6O)nCOOH, to the viscoelastic solution decreases the viscosity monotonically until phase separation. On the other hand, when perfluorodecalin oil, C10F18, is added, viscosity first decreases and attains a limiting value before excess oil phase separates out. The viscosity decrease in water/surfactant/oil systems is possibly caused by the microstructural transition in the network structure. Small-angle X-ray scattering (SAXS) measurements were performed to complement the rheological data. It has been found that the C8F17EO3 induces one-dimensional growth to the C8F17EO20 micelles. On the other hand, when (C3F6O)nCOOH is added, wormlike-sphere type transition is more likely to occur.