A class of "naked" AGN has been reported (Hawkins 2004), characterized by strong amplitude optical brightness variability and the complete absence of broad emission lines in the optical spectrum. The optical variability suggests that the nucleus is seen directly, while the absence of broad lines contradicts the simple formulation of Unified Models for AGN. We observed quasi simultaneously in X-rays (XMM-Newton) and optical (NTT, La Silla) two "naked" AGN, confirming the "naked" nature of Q2131-427 for which no broad emission line components have been detected in the optical spectrum and its X-ray spectrum shows no signs of intrinsic absorption. The optical and X-ray mismatch in this source cannot be ascribed to a high nuclear dust-to-gas ratio and a Compton Thick nature is ruled out. We suggest that the Broad Line Region (BLR) may be completely absent in this source, possibly as a consequence of its low Eddington ratio. The second "naked" AGN candidate, Q2130-431, shows Hα and Hβ broad emission line components in its optical spectrum, revealing the presence of a BLR. A mild X-ray absorption is expected in intermediate type 1.8 Seyfert galaxies like Q2130-431, however we put a very low upper limit on the column density, also the low Balmer decrement suggests that the BLR itself does not suffer from reddening. We propose that in this object the BLR is instrinsecally weak, making a case of "true" intermediate Seyfert galaxy.