We establish polynomial-time convergence of infeasible-interior-point methods for conic programs over symmetric cones using a wide neighborhood of the central path. The convergence is shown for a commutative family of search directions used in Schmieta and Alizadeh [9]. These conic programs include linear and semidefinite programs. This extends the work of Rangarajan and Todd [8], which established convergence of infeasible-interior-point methods for self-scaled conic programs using the NT direction.