By applying a new method for aberration derivation to anamorphic systems made from cylindrical surfaces, we obtain a complete set of primary aberration coefficients. This set is in a form similar to the well-known Seidel aberrations for rotationally symmetrical optical systems (RSOS). The aberration coefficients include first-order quantities only. By tracing four nonskew paraxial marginal and chief rays in the two associated RSOS of the anamorphic system, the aberration coefficients can be derived.