Ideal magnetohydrodynamic stability analysis of local pressure-driven modes in an L=1 heliotron, Heliotron J [M. Wakatani , Nucl. Fusion 40, 569 (2000)], is investigated by means of three-dimensional (3D) ballooning formalism and the Mercier criterion. In 3D systems such as heliotrons, the ballooning modes are separated into two categories: One is tokamak-like ballooning modes which are localized only in the poloidal direction, and the other is modes inherent to 3D systems which are localized on the specific flux tubes. The tokamak-like ballooning modes change to the Mercier modes in the limit that the mode is sufficiently extended along the field line, but the nonaxisymmetric ballooning mode does not so. The L=1 Heliotron J equilibrium investigated here has weak global shear and the dominant Fourier amplitudes of magnetic-field strength is rather different from the conventional helical systems with L=2 helical coils. Since the weak global shear causes the reduction of integrated local shear along the field lines easily, which combines with strongly modulated destabilizing effects on the flux surface, the nonaxisymmetric ballooning modes localized on the specific flux tubes can become unstable. On the other hand, the Mercier modes are suppressed due to the deep magnetic well. The results obtained from the model equilibrium of L=2 Large Helical Device (LHD), for which several reports have already published [N. Nakajima, Phys. Plasmas 3, 4556 (1996), for example], are also shown and compared with the results of Heliotron J. The LHD equilibrium employed here has a magnetic hill region at the outer radius, and this tends to make the Mercier modes unstable. It is found that this difference of the Mercier stability property in two equilibria is concerned in the local ballooning stability, and the notable difference of local dispersion relations appears. It is also found from the comparison of two systems that the nonaxisymmetric ballooning modes have a similar property to the tokamak-like ballooning modes, in the sense of the (s) over bar- <(<alpha>)over bar> diagram where (s) over bar and <(<alpha>)over bar> are shear and pressure gradient parameter. (C) 2001 American Institute of Physics.