Two-particle correlations in pPb collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV are studied as a function of the pseudorapidity separation (Delta eta) of the particle pair at small relative azimuthal angle (|Delta phi| < pi/3). The correlations are decomposed into a jet component that dominates the short-range correlations (|Delta eta| < 1), and a component that persists at large Delta eta and may originate from collective behavior of the produced system. The events are classified in terms of the multiplicity of the produced particles. Finite azimuthal anisotropies are observed in high-multiplicity events. The second and third Fourier components of the particle-pair azimuthal correlations, V2 and V3, are extracted after subtraction of the jet component. The single-particle anisotropy parameters v2 and v3 are normalized by their laboratory frame midrapidity value and are studied as a function of eta(c.m). The normalized v2 distribution is found to be asymmetric about eta(c.m.) = 0, with smaller values observed at forward pseudorapidity, corresponding to the direction of the proton beam, while no significant pseudorapidity dependence is observed for the normalized v3 distribution within the statistical uncertainties.