The mean-field phase diagram of a three-dimensional axial-next-nearest-neighbor Ising (ANNNI) model in a transverse field has been studied here. The dynamical modes are found by using the random-phase approximation and the phase diagram is also obtained from the softening condition of these modes. For a one-dimensional ANNNI model in a transverse field, these dynamical modes are obtained here more accurately using a Jordan-Wigner-type transformation (with some approximations). Softening of these modes gives the zero-temperature phase diagram in one dimension.