The extremely asymmetrical scattering (EAS) of bulk and guided electromagnetic waves in nonuniform periodic Bragg arrays with steplike variations of the grating amplitude is analyzed theoretically by means of a recently developed approach based on allowance for the diffractional divergence of the scattered wave. Arrays of finite and infinite widths are investigated. It is shown that, for thin nonuniform arrays, EAS has the same pattern as for uniform arrays with mean grating amplitude. On the contrary, for wide nonuniform arrays, the scattered wave amplitudes are well determined by local values of the grating amplitude. In this case, the energy of the scattered wave is shown to concentrate mainly in regions with smaller grating amplitude. The sensitivity of EAS to small imperfections of periodic arrays is investigated theoretically. The physical explanation of the observed effects is based on the diffractional divergence of the scattered wave.