The paper discusses a homogeneous one-dimensional pseudodifferential equation with a symbol of the form
A(x,ξ)=A0(ξ)+∑k=1Nthπα(x−λk+iαβ2)Ak(ξ)
(x,ξ,λ∈R,α>0,−1<β<1,k=1,2,…,N),
where Ak(ξ)(k=0,1,...,N) are locally integrable functions from class of symbols of non-negative order r . The method of bringing the pseudodifferential equation to a system of onedimensional singular integral equations with Cauchy’s kernel is proposed.