Spatially localized moving and stationary pH patterns are generated in two-side-fed reaction-diffusion systems. The patterns are sandwiched between two quiescent zones and positioned by the antagonistic gradients of the reactants of the self-activatory process. Spatial bistability, spatiotemporal oscillations, and formation of stationary Turing patterns have been predicted by numerical simulations and observed in experiments performed by using different hydrogen ion autocatalytic chemical systems. The formation of stationary patterns due to long-range inhibition is promoted by a large molecular weight hydrogen ion binding polymer.