In response to 6-10-ns laser irradiation of nematic liquid- crystal layers, unusual approximately 0.5 - ten second build-up time, high-contrast, far-field, concentric elliptical diffraction rings in a 532-nm, linearly polarized, Gaussian beams, are observed at 2 - 10-Hz pulse- repetition rate, a phenomenon strongly dependent on the orientation of the nematic molecules, under experimental conditions excluding ordinary orientational spatial self- phase modulation, for a geometry in which incident laser- light polarization is parallel to the nematic director and propagation direction perpendicular to the planar-nematic cell. Once formed, each set of rings may, upon further irradiation, exist for up to several minutes. The number of these rings varies systematically with laser intensity (between 1 - 2 and (up to) 20 rings). Cells of nematic 5CB (or its mixture with 7 CB) with 30, 50, 105, or 125-micrometers thickness and laser-beam diameters (at 1/e2 level) of approximately 35 - 50 and 160-micrometers are used. The threshold of the nonlinearity is modified either by changing the laser repetition rate or by adding a two-photon absorbing chromophore. For CW laser irradiation of twice higher power density than the average power density in the pulsed mode the effect disappears.