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This work reports on three projects undertaken with the aim of learning more about complex behavior such as multiple steady states in a CSTR and traveling waves and spatial structures in unstirred solutions. Bistability in the permanganate-oxalate system was studied spectrophotometrically and computationally using a CSTR in a UV-Vis spectrophotometer. Absorbance of the solution was monitored as a function of flow rate. The concentrations of several manganese containing species in each of the steady states at a specific flow rate were determined using multi-component analysis. A four-variable empirical rate law model and computational results were presented. An experimental investigation of relaxation behavior in the bistable iodate-arsenous acid system revealed a region of flow rates where the system exhibited an apparent metastable steady state. Since this state appears as a plateau in a plot of iodide concentration vs. time, the region is called the plateau region. Relaxation times were measured and the limits of the plateau region determined. The relaxations have the form {dollar}\au{dollar} = c(k{dollar}\\sb{lcub}0{rcub})\\sp{lcub}\\rm -z{rcub}{dollar}, where c is a constant, z is the critical exponent, k{dollar}\\sb{lcub}0{rcub}{dollar} = {dollar}\\vert\\rm k\\sb{lcub}0{rcub} - k\\sbsp{lcub}0{rcub}{lcub}\\rm t{rcub} \\vert{dollar}, and k{dollar}\\sbsp{lcub}0{rcub}{lcub}\\rm t{rcub}{dollar} is the reciprocal residence time of the transition point. The experimental value of the critical exponent was evaluated. Relaxation times and the value of the critical exponent were determined using both a numerical integration method and an analytical solution of a simple one-variable model of the iodate-arsenous acid system. The experimental and computational results were found to be in good agreement. The development of a two-dimensional spectrophotometer for the study of chemical waves and spatial structures was described. The system was applied to the Belousov-Zhabotinskii reaction using an immobilized ferroin catalyst. Broken spirals and spatial turbulence were discovered and characterized.