A (GGGGCC) hexanucleotide repeat (HR) expansion in the C9ORF72 gene has been considered the major cause behind both frontotemporal dementia and amyotrophic lateral sclerosis, while a (GGGCCT) is associated with spinocerebellar ataxia 36. Recent experiments involving NMR, CD, optical melting and 1D (1)H NMR spectroscopy, suggest that the r(GGGGCC) HR can adopt a hairpin structure with G-G mismatches in equilibrium with a G-quadruplex structure. G-Quadruplexes have also been identified for d(GGGGCC). As these experiments lack molecular resolution, we have used molecular dynamics microsecond simulations to obtain a structural characterization of the G-quadruplexes associated with both HRs. All DNA G-quadruplexes, parallel or antiparallel, with or without loops are stable, while only parallel and one antiparallel (stabilized by diagonal loops) RNA G-quadruplexes are stable. It is known that antiparallel G-quadruplexes require alternating guanines to be in a syn conformation that is hindered by the C3'-endo pucker preferred by RNA. Initial RNA antiparallel quadruplexes built with C2'-endo sugars evolve such that the transition (C2'-endo)-to-(C3'-endo) triggers unwinding and buckling of the flat G-tetrads, resulting in the unfolding of the RNA antiparallel quadruplex. Finally, a parallel G-quadruplex stabilizes an adjacent C-tetrad in both DNA and RNA (thus effectively becoming a mixed quadruplex of 5 layers). The C-tetrad is stabilized by the stacking interactions with the preceding G-tetrad, by cyclical hydrogen bonds C(N4)-(O2), and by an ion between the G-tetrad and the C-tetrad. In addition, antiparallel DNA G-quadruplexes also stabilize flat C-layers at the ends of the quadruplexes.