Two recurrent novae (RNe) that do not host red giants were observed in outburst at the beginning of 2009 and 2010, respectively. The first nova was LMC 2009a, and the second one was U Scorpii. Nova LMC 2009a was a relatively slow RN, and it was quite luminous both at optical and X-ray wavelengths. U Sco is the fastest nova ever recorded. Its supersoft X-ray phase started a couple of weeks after optical maximum and lasted for about a month, while for Nova LMC 2009a this phase started four months after maximum and lasted for 5 months. For both novae, the first X-ray spectrum taken while the luminous supersoft X-ray source was beginning to emerge is remarkably similar with broad and prominent emission lines of nitrogen and carbon accounting for at least 30% of the X-ray flux. Blue-shifted absorption and red-shifted emission form apparent P-Cyg profiles. We attribute the emission features to the ejecta and show evidence that they are largely due to collisional ionization. In the case of U Sco the absorption lines were embedded in the emission features after the first observation. We find evidence that in U Scorpii we were observing the Thomson reflected spectrum at a distance of ≃ 3 R⊙ from the white dwarf rather than the atmosphere itself. For both novae, the peak temperature was remarkably high, probably close to 900,000 K for U Sco, and about 600,000 K for Nova LMC 2009a. We suggest that these two objects represent different stages of RNe secular evolution.