Instability of liquid crystal membranes with respect to spontaneous rolling up into cylinders or double cylinders and their subsequent Very complicated evolution and also phase transition within cores are reported in the present paper. We have investigated here the formation and spontaneous evolution of liquid crystal membranes and filamentary structures in nematosmectogen 4-nitrophenyl-4'-actyloxybenzoate (NPOOB) dissolved in hydrophobic silicone oil H (SO). The first-type phase transitions are observed here within the filaments produced in system composed of 4-acetyl-4'-dodecylbiphenyl (Bg) and 4,4 " -pentylcyclohexyl(4'-pentylcyclohexyl) benzoate (B10) dissolved in SO. We discuss crude continuum model of the instability of liquid crystal membranes with asymmetric surface tension and the influence of the pressure exerted by such a tension on the phase behavior within the filaments. The fringe-field microinterferometric analysis has provided decisive evidence of the homeotropic organization of the membranes, planar ordering within the cylinders and of bifilar model of the filaments.