Algorthims for Computing Heteroclinic Orbits Heteroclinic orbits play an important role in nonlinear Differential Equations. They arise for example, as traveling wave solutions of partial differential equations. The applications include soliton propagation along optical fibers, electrical circuits and neural models. Heteroclinic orbits (which are orbits of infinite period) connect fixed points of a vector field. In this work we compute heteroclinic orbits for the Morris-Lecar equations, which model neural behavior in a barnacle muscle fiber. Two algorithms which trace out branches of heteroclinic orbits between a saddle node and a stable node are described and the results obtained are compared. The software packages AUTO and KAOS were used for the computations.