- The two variable expansion method is used to study the stability of infinitesimal motions about the triangular libration points in the elliptic restricted problem of three bodies. This perturbation technique entails replacing the independent variable (here f, the true anomaly of the smaller primary) with two new independent variables. The results of the study are analytical expressions for the transition curves bounding regions of stability in the e plane, accurate to 0(e3). For small e, these expressions are seen to compare favorably with the numerical analysis of Danby. 1969 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.