We consider the operator L generated in L2(ℝ+) by the differential expression l(y)=-y′+q(x)y, x ∈ ℝ+:=[0,∞) and the boundary condition y′(0)/y(0) = α0 + α1λ+ α2λ 2, where q is a complex-valued function and αi ∈ ℂ, i=0,1,2 with α2 ≠ 0. In this paper we obtain the properties of the principal functions corresponding to the spectral singularities of L. © 2011 Nihal Yoku.