Abstract <p>This paper studies the nonhomogeneous Hilbert boundary value problem in the half-plane with a finite index for a single generalized Cauchy–Riemann equation with a strong singularity in the coefficient. A formula for the solution to this equation is derived, and the solvability of the Hilbert problem for analytic functions with an infinite index and two vortex points of power and logarithmic orders is investigated. Based on this, the solvability of the Hilbert boundary value problem for generalized analytic functions is studied.</p>