  In this paper we study resonances of the $ABC$-flow in the near integrable
case ($C\ll 1$). This is an interesting example of a Hamiltonian system with
3/2 degrees of freedom in which simultaneous existence of two resonances of the
same order is possible. Analytical conditions of the resonance existence are
received. It is shown numerically that the largest $n:1$ ($n=1,2,3$) resonances
exist, and their energies are equal to theoretical energies in the near
integrable case. We provide analytical and numerical evidences for existence of
two branches of the two largest $n:1$ ($n=1,2$) resonances in the region of
finite motion.
