Phase diagram investigations of symmetric microemulsions of water-n-decane-C10E4-PEP5-PEO5 in the semidilute regime suggested the existence of anisotropic mesophases (C10E4, n-decyl tetraoxyethylene glycol ether; PEP5-PEO5, poly(ethylenepropylene)-co-poly(ethylene oxide), M-PEP = M-PEO = 5 kg mol(-1)). Performing a temperature scan on a sample at fixed composition, we observed an alternating sequence of eight two-phase regions and six one-phase regions. The composition of the sample was chosen to contain equal volumes of water and oil and an overall weight fraction of surfactant and polymer of 0.20. We examined the nature of the lyotropic mesophases and the coexisting phases by measuring the line splitting of H-2 NMR spectra. The experiments unequivocally reveal the existence not only of a lamellar (L-alpha) but also of a normal hexagonal (H-1) and a reverse hexagonal (H-2) phase.