In this paper almost C(λ)-manifolds are considered. The local structure of Ricci-flat almost C(λ)-manifolds is obtained. On the space of the adjoint G-structure, necessary and sufficient conditions are obtained under which the al-most C(λ)-manifolds are manifolds of constant curvature and the structure of the Riemannian curvature tensor of an almost C(λ)-manifold of constant curvature is obtained. Relations are obtained that characterize the Einstein almost C(λ)-manifolds. It is proved that a complete almost C(λ)-Einstein manifold is either holomorphically isometrically covered by the product of a real line by a Ricciflat Kähler manifold, or is compact and has a finite fundamental group. For almost C(λ)-manifolds that are -Einstein, analytic expressions for the functions and characterizing these manifolds are obtained. It is shown that an almost C(λ)-manifold has an Ф-invariant Ricci tensor. We study also almost C(λ)-manifolds of pointwise constant Ф-holomorphic sectional curvature.