Cylindrical acoustic waveguides with constant cross-section ω are considered, specifically, a straight waveguide Ω = R × ω ⊂ R^d and a locally curved waveguide Ω^ε that depends on a parameter ε ∈ (0, 1]. For d > 2, in two different settings (ε = 1 and ε ≪ 1), the task is to find an eigenvalue λ^ε that is embedded in the continuous spectrum [0,+∞) of the waveguide Ω^ε and, hence, is inherently unstable. In other words, a solution of the Neumann problem for the Helmholtz operator Δ + λ^ε arises that vanishes at infinity and implies an eigenfunction in the Sobolev space H¹(Ω^ε). In the first case, it is assumed that the cross-section ω has a double symmetry and an eigenvalue arises for any nontrivial curvature of the axis of the waveguide Ω^ε. In the second case, under an assumption on the shape of an asymmetric cross-section ω, the eigenvalue λ^ε is formed by scrupulous fitting of the curvature O(ε) for small ε > 0.