A Korteweg–de Vries equation that is applicable to both the nonlinear magnetosonic fast and slow waves is derived from a two‐fluid model with finite ion and electron pressures. As in the cold plasma theory, the fast wave has a critical angle &thgr;c. For propagation angles greater than &thgr;c(quasiperpendicular propagation), the fast wave has a positive soliton, whereas for angles smaller than &thgr;c, it has a negative soliton. Finite  &bgr; effects decrease the value of &thgr;c. The slow wave has a positive soliton for all angles of propagation. The magnitude of resonant ion acceleration (thevp×Bacceleration) by the nonlinear fast and slow waves is evaluated. In the fast wave, the electron pressure makes the acceleration stronger for all propagation angles. The decrease in &thgr;cresulting from finite  &bgr; effects results in broadening of the region of strong acceleration. It is also found that fairly strong ion acceleration can occur in the nonlinear slow wave in high  &bgr; plasmas. The possibility of unlimited acceleration of ions by quasiperpendicular magnetosonic fast waves is discussed.