The first part of this article (Sections I and II) presents oneself an overview of theory and phenomenology of truly neutral particles based on the papers of Majorana, Racah, Furry, McLennan and Case. The recent development of the construct, undertaken by Ahluwalia [Mod. Phys. Lett. A9 (1994) 439; Acta Phys. Polon. B25 (1994) 1267; Preprints LANL LA-UR-94-1252, LA-UR-94-3118], could be relevant for explanation of the present experimental situation in neutrino physics and astrophysics.In Section III the new fundamental wave equations for self/anti-self conjugate type-II spinors, proposed by Ahluwalia, are re-casted to covariant form. The connection with the Foldy-Nigam-Bargmann-Wightman-Wigner (FNBWW) type quantum field theory is found. The possible applications to the problem of neutrino oscillations are discussed. ul., 83, Saratov RUSSIA. Internet address: dvoeglazov@main1.jinr.dubna.su 1 There are opposite opinions on the solar neutrino problems. E. g., in his talk "The steady vanishing of the three solar neutrino problems" at the 27th Int. Conf. on High Energy Physics (1994) Prof. D. R. O. Morrison denies [5] their existence at all: "The evidence for any solar neutrino problem is "not compelling".2 Thanks to the two-component neutrino theory proposed by Landau, Lee, Yang and Salam [30].3 Surprisingly, the six of the present upper bounds on m 2 νe are negative [31]. E. g., the LANL result is −147 ± 68 ± 41 eV 2 , the LLNL one, −130 ± 20 ± 15 eV 2 . The most recent measurement (Troitsk, 1994) involves a new kind of systematics and gives −18 ± 6 eV 2 .