  We study local analytical integrability in a neighborhood of $p:-q$ resonant
singular point of a two-dimensional vector field and its connection to
time-reversibility with respect to the non-smooth involution $
\varphi(x,y)=(y^{p/q},x^{q/p}). $ Some generalizations of the theory developed
by K.~S.~Sibirsky for $1:-1$ resonant case to the $p:-q$ resonant case are
presented.
