This paper presents the derivation of the nonlocal equations for curved beams with varying curvature and cross-section. Eringen's nonlocal constitutive equations are rewritten in cylindrical coordinates and implemented into the classical beam equations considering the effects of axial extension and the shear deformation. Varying distributed loads are also considered in the equations. The governing differential equations of an arbitrary curved beam bearing variable distributed loads are solved exactly by using the initial value method. The displacements, rotation angle about the binormal axis and the force resultants are obtained analytically. The nonlocal equations include the length scale parameter which is also known as nonlocal parameter. Several numerical examples are solved to emphasize the effect of the length scale parameter. A parametric study is also performed to point out the effects of the slenderness ratio, opening angle, loading and boundary conditions and also axial and shear deformations on the static behavior of the beam.