An axisymmetrical flow of a two-layer capillary jet is studied. The most general formulation of the jet instability problem is considered. The influence of the governing parameters on the amplification factor of the disturbances is investigated taking into account the variation along the jet of the main how velocity profile. The boundary layer approximation to full Navier-Stokes formulation is applied for calculation of a stationary mean flow. Stability analysis is carried out for various cross sections along the jet on the assumption of a locally parallel main flow. Numerical calculations of the corresponding eigenvalue problem reveal two types of unstable perturbations connected with the presence of the free surface and interface accordingly. The predominant type of instability is defined by the main flow properties. Numerous solutions of the multiparameter stability problem are presented.