The stability of internal, ideal modes in tokamaks with low magnetic shear in the plasma core is analyzed. For equilibria with large aspect ratio, a parabolic pressure profile and a flat q profile in the core, an exact solution of the ideal magnetohydrodynamic (MHD) stability equations is found. The solution includes the eigenfunctions and the complete spectra of two distinctly different MHD phenomena: A family of fast-growing, Mercier-unstable global eigenmodes localized in a low-shear region with q < 1, and another, related family of stable, global eigenmodes existing in plasmas with q>1 in the core. In the latter case the solution in addition includes one unstable eigenmode, if beta is larger than a critical value depending on the width of the low-shear region and on the q-profile in the edge region. (C)2007 American Institute of Physics.