A calculation is presented that accounts for rapid nonlinear growth of them=1 kink‐tearing instability. The equilibrium analysis contained in the Rutherford theory [Phys. Fluids16, 1903 (1973)] of nonlinear tearing‐mode growth is generalized to islands for which the constant‐&psgr; approximation is not valid. Applying the helicity‐conservation assumption introduced by Kadomtsev [PlasmaPhysicsandControlledNuclearFusionResearch(IAEA, Vienna, 1977), Vol. I, p. 555], the presence of a current‐sheet singularity is shown that gives rise to a narrow tearing layer and rapid reconnection. This rapid reconnection, in turn, justifies the use of the helicity conservation assumption. The existence of a family of self‐similarm=1 equilibrium islands is demonstrated. The formalism introduced here is shown to apply both to the case of them=1 kink‐tearing mode and to the case of forced reconnection. These two cases are compared and contrasted.