New spectra of the Type Ic supernovae 1997B and 1997X at nebular phase are shown. Although one of them, SN 1997X, was studied with some detail around its maximum and its properties compared with other well-known SNe Ib/c, both of these events were later followed within its nebular phase. Our aim is to explore the behavior of these supernovae when they reached the nebular phase. Comparisons with data of other SNe Ic at similar nebular phases, mainly by using spectra from the Canarias Database, are also performed. The results derived from these comparisons reinforce the quite heterogeneous behavior found in SNe Ic nebular spectra. In particular, the widths of the [O I] and [Ca II] emissions found in SN 1997B are wider than the average for Type Ic events, while the [O I] width of SN 1997X is narrower than the average and is nearly comparable to typical [O I] widths found in SNe Ib. Based on observations made with the 2.5 m Isaac Newton Telescope and the 4.2 m William Herschel Telescope operated on La Palma by the Isaac Newton Group of Telescopes at Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias.