Steady laminar flows in coiled annular ducts are investigated numerically. Numerical solutions are obtained by solving the incompressible Navier-Stokes equation with a SIMPLE type procedure for annular curved ducts of various radius ratio for a given Reynolds number. Effect of radius ratio on the flow development is given particular attention. Computational results indicate that the secondary flow in a half cross section (above or below the line of symmetry) for the case of moderate radius ratio is characterized by a pair of counter-rotating vortices; the flow in the core region is toward the outside bend and the flow near the inner and outer walls is toward the inside bend. However, when the radius ratio is very large, say greater than 0.8, the secondary flow is unidirectional and is toward the inside bend, owing to the strong viscous effect. It is also found that the downstream flow development is greatly affected by the radius ratio. When the radius ratio is moderate, the centroid of the first moment of streamwise velocity lies on the outside half plane; when the radius ratio is very large, the centroid lies on the inside half plane. In contrast to the case of straight annular duct, the flow in a curved annular duct is not necessarily fully developed earlier when the radius ratio is larger owing to the complicated interaction between the viscous and the centrifugal forces.