The work studies the effect of stable ion confinement in periodic and nonuniform electrostatic fields. As an example of periodic systems, there are considered ion guides formed by a sequence of lenses as well as electrostatic traps and multireflecting time-of-flight mass spectrometers formed by ion mirrors. Using a first-order approximation, it is shown that cylindrical and planar symmetric periodic fields have focusing properties and retain ions near the axis of symmetry in a wide range of energies. A new term "effective retaining potential" is introduced to characterize stability of ion motion as an ability to withstand external perturbations like electrostatic or magnetic deflection as well as random ion scattering. Effects of nonlinear terms are observed. It is shown that compensation of chromatic aberrations improves ion stability in reflecting periodic systems.