The evolution of the meanders on reaches of 10 alluvial streams in the United States is reconstructed, and a scheme for the evolution and classification of meander loops, derived from a study of the meandering pattern of 125 alluvial streams, is proposed. In the main evolutionary trend, a low symmetrical arc of approximately constant curvature tends to increase in height but decrease in radius as it grows. When its length exceeds its radius, the arc is termed a simple symmetrical meander loop. A simple loop becomes asymmetrical by the growth on its perimeter of a second arc of constant curvature, which is commonly tangent to the first and curved toward the same side of the stream. A simple loop becomes compound when a second arc on its perimeter has developed into a loop. Four main categories of loops (simple symmetrical, simple asymmetrical, compound symmetrical, and compound asymmetrical) and about 16 form types are proposed. The compound loops are regarded as aberrant forms of indefinite radius and length, but the meandering patterns can be analyzed into simple loops whose properties can be measured and treated statistically.