The zero-temperature dynamical properties of the one-dimensional Ising model with exchange constant J in a skew uniform magnetic field (Hx,Hz) are given by analytic expressions neglecting corrections of order (Hx/J)2 and (Hz/J)2. The lowest multiplet of the excitation spectrum and the transverse frequency and wavenumber dependent susceptibility are expressed in terms of Bessel functions. In a small longitudinal field the excitation spectrum has a multibranch structure which for vanishing longitudinal field merges into a band. The singular character of the transition between the semi-infinite discrete spectrum and the band gives rise to a power-law behaviour. The energy levels depend on Hx to the power 1/3 and on Hz to the power 2/3. An experimental search for systems revealing the above effects is suggested.