The equivalent lens conversion technique is applied to design achromatic doublet and aplanatic doublet. A thin doublet which has zero axial thicknesses, are corrected for the third order aberrations at first, and the thin doublet is converted into thick lens system by using the equivalent lens conversion. Two types of cemented doublets, the Fraunhofer type and the Steinheil type, are designed by using a crown glass BaK-2 and a flint glass SF-2. In the thin doublet design, there are two achromatic solutions and a aplanatic solution for the both types.