Magnetic flux tubes (slabs or cylinders) are of considerable physical interest because of their occurrence in the sun’s atmosphere. The propagation of weakly nonlinear, long‐wavelength (weakly dispersive), sound waves in both a magnetic slab and a magnetic cylinder is discussed. The slab geometry leads to the Benjamin–Ono equation, viz., ∂v/∂t+cT(∂v/∂z) +&bgr;v(∂v/∂z) +(&agr;/&pgr;)(∂2/∂z2) ×∫&slash;∞−∞[v(s,t)ds/(s−z)]=0, and the cylindrical geometry yields its allied form, viz., ∂v/∂t+cT(∂v/∂z)+&bgr;v(∂v/∂z) +&agr;’(∂3/∂z3)∫∞−∞{v(s,t)ds/ [&lgr;2+(s−z)2]1/2}=0, an equation known also to arise in waves on concentrated vortices in fluids. The magnetic flux tube thus provides a simple illustration of these two equations, hitherto only considered in separate physical systems.