An asymptotic model is developed to study magnetohydrodynamic equilibria in toroidal systems with a helical magnetic axis. Using a characteristic coordinate system based on the vacuum field lines, the equilibrium problem is reduced to a two‐dimensional generalized partial differential equation of the Grad–Shafranov type. A stellarator‐expansion free‐boundary equilibrium code is modified to solve the helical‐axis equations. The expansion model is used to predict the equilibrium properties of toroidal asperator devices. Numerically determined flux surfaces, magnetic well, transform, and shear are presented. The equilibria show a toroidal Shafranov shift.