Using fiberings, we determine the cup-length and the Lyusternik-Shnirel’man category for some infinite families of real flag manifolds $O(n₁+...+n_q)/O\left(n₁\right)\times ...\times O\left(n_q\right)$, q ≥ 3. We also give, or describe ways to obtain, interesting estimates for the cup-length of any $O(n₁+...+n_q)/O\left(n₁\right)\times ...\times O\left(n_q\right)$, q ≥ 3. To present another approach (combining well with the “method of fiberings”), we generalize to the real flag manifolds Stong’s approach used for calculations in the ℤ₂-cohomology algebra of the Grassmann manifolds.