We discuss novel features of a new continuum RPA formulated in the coordinate-space Hartree-Fock-Bogoliubov framework. This continuum quasiparticle RPA takes into account both the one-and two-particle escaping channels. The theory is tested with numerical calculations for monopole, dipole and quadrupole excitations in neutron-rich oxygen isotopes near the drip-line. Effects of the particle-particle RPA correlation caused by the pairing interaction are discussed in detail, and importance of the selfconsistent treatment is emphasized. §1. IntroductionCollective excitation in unstable nuclei is one of the most attractive subjects since the exotic structures in the ground state, such as halo, skin, and the presence of loosely bound nucleons, may cause new features in the excitations, e.g. the lowenergy dipole mode that is being discussed extensively. The random phase approximation (RPA) or the linear response theory is one of the most powerful framework to investigate such problems microscopically. Indeed the continuum RPA theory in the coordinate-space representation 1), 2) has played major roles so far since it can describe the continuum states crucial for nuclei near drip-line.The pairing correlation is another key feature of drip-line nuclei. 6) -8) To treat the coupling of the continuum states as well as the density dependence of the pairing correlation, the Hartree-Fock-Bogoliubov (HFB) theory formulated in the coordinate-space representation 6), 9) has been developed while the conventional BCS approximation has inherent deficiency.It is therefore important to combine the continuum RPA and the coordinate space HFB in a consistent way in order to describe the excitations in unstable nuclei near drip-line, especially when the pairing correlation play crucial roles. We have recently shown that a new quasiparticle RPA (QRPA) satisfying this requirement is indeed possible. 10) In the present paper, we discuss characteristic features of the theory and analyze excitations of near-drip-line nuclei, focusing on effects of the pairing, by using numerical calculations performed for the monopole, dipole and quadrupole excitations in neutron-rich oxygen isotopes. The previous continuum QRPA approaches employ the BCS approximation. 11) -14) Other QRPA approaches applied to unstable nuclei neglect the escaping effects since some use the BCS quasiparticle basis, 15) -17) and other adopt the coordinate-space HFB but use the discretized canonical basis. 18) The present formalism provides the first consistent continuum * )