The equations describing the behavior of a electronic circuit are nonlinear due to nonlinear elements and the DC analysis is the first step for analyzing a nonlinear circuit and also to find the solution, or solutions, of the system of equations. Methods like Newton Raphson algorithm present disadvantages to solve nonlinear problems besides are not capable to find multiple solutions. To overcome above problems the homotopy methods can locate multiple solutions for a system of equations; however homotopy methods convergence depends of the starting point, the continuous methods and nonlinearities. The homotopy formulation require suitable path tracking techniques to accurately trace the homotopy curve, the algorithm to path-tracking used in this work is the spherical algorithm because it is geometrically clear and this characteristic can facilitate its programming. However during programming hyperspheres method there were some problems as reversion of the path on the curve and slow for tracing. In this thesis, two proposed methodologies are used to solve the above problems, the first proposed methodology is based in calculating the normal vector to the curve for detecting the problem of reversion then the methodology is used to avoid the problem of reversion. The second methodology is achieved during the tracing of the homotopy curve to reduce the number of iterations and the computational time. Both strategies are implemented and programmed for the hyperspheres method; also several case studies are solved, and we found satisfactory results for the path tracking problem.