Poly-glycine-alanine (poly-GA) proteins are widely believed to be one of the main toxic dipeptide repeat molecules associated with amyotrophic lateral sclerosis (ALS) and frontotemporal dementia diseases. Using discontinuous molecular dynamics simulation and an all-atom model of the proteins, we study folding, stability, and aggregation of poly-GA. The results demonstrate that poly-GA is an aggregation-prone protein that, after a long enough time, forms β-sheet-rich aggregates that match recent experiment data and that two unique helical structures are formed very frequently, namely, β-helix and double-helix. The details of the two structures are analyzed. The analysis indicates that such helical structures are stable and share the characteristics of both α-helices and β-sheets. Molecular simulations indicate that identical phenomena also occur in the aggregation of poly-glycine-arginine (poly-GR). Therefore, we hypothesize that proteins of type (GX)n in which X may be any non-glycine amino acid and n is the repeat length may share the same folding structures of β-helix and double-helix and that it is the glycine in the repeat that contributes the most to this characteristic. Molecular dynamics simulation with continuous interaction potentials and explicit water molecules as the solvent supports the hypothesis. To our knowledge, this is the first molecular dynamics simulation of the phenomena involving poly-GA and poly-GR proteins.