The matrizant of the two-body problem is developed in terms of elements that are free from singularities for zero eccentricities and zero- and ninety-degree inclinations. Retrograde equinoctial elements eliminate the singularity for inclinations near 180 degrees, with only minor changes in the expressions for the matrizant. The 'single-averaged' variation-of-parameters equations for these elements are developed for third-body, oblateness, and drag effects. Higher order terms are included in the expansions for the third-body and oblateness potential. A computer program that uses these equations to predict orbital evolution is described. Numerical results are given for a near-circular orbit.