RecentlyPrus-Wiśniowski  has proved that the continuous functions of Λ-bounded variation on [0, 1] form a set of the first category in the Banach
space C[0, 1] and also in each Banach space CΓBV[0, 1] of continuous functions of Γ-bounded variation on [0, 1] provided that
the sequence Γ is adequate. In the present paper these results are extended and completed by using a principle of the condensation
of the singularities of a family of nonnegative functions that follows from the theorems given byBreckner . It is shown that Baire category properties similar to those stated in  are valid for two very large classes of real-valued
functions called functions of bounded λ-variation of orderp and functions of boundedmth variation of orderp, respectively. The benefit of considering these classes is that they comprise several classes of functions of bounded variation
type which have occurred so far in Fourier analysis or real analysis; in particular, the functions investigated in . Thus,
by specializing the results derived in the present paper, they give at once Baire category information concerning a number
of well-known sets of real-valued functions.