Neutrino Anomalies and Quasi-Dirac Neutrinos

We discuss possibility of describing solar, atmospheric and LSND results with four neutrinos forming two quasi-degenerate pairs. The simplest versions of this 2+2 scheme with either $\nu_e$ or $\nu_\mu$ mixing exclusively with sterile neutrino is disfavored by the SNO and atmospheric neutrino results respectively. A generalized scheme with sterile state participating in both the solar and atmospheric oscillations is still allowed. We show that the complex pattern of mixing needed for this purpose follows from a simple L_e+L_\mu-L_\tau-L_s symmetry. Specific form of L_e+L_\mu-L_\tau-L_s symmetric mass matrix is determined from experimental results. Two theoretical schemes which lead to this form and a proper breaking of L_e+L_\mu-L_\tau-L_s symmetry are discussed.