We have characterized the conformational ensembles of polyglutamine peptides of various lengths (ranging from to ), both with and without the presence of a C-terminal polyproline hexapeptide. For this, we used state-of-the-art molecular dynamics simulations combined with a novel statistical analysis to characterize the various properties of the backbone dihedral angles and secondary structural motifs of the glutamine residues. For (i.e., just above the pathological length for Huntington’s disease), the equilibrium conformations of the monomer consist primarily of disordered, compact structures with non-negligible -helical and turn content. We also observed a relatively small population of extended structures suitable for forming aggregates including – and -strands, and – and -hairpins. Most importantly, for we find that there exists a long-range correlation (ranging for at least residues) among the backbone dihedral angles of the Q residues. For polyglutamine peptides below the pathological length, the population of the extended strands and hairpins is considerably smaller, and the correlations are short-range (at most residues apart). Adding a C-terminal hexaproline to suppresses both the population of these rare motifs and the long-range correlation of the dihedral angles. We argue that the long-range correlation of the polyglutamine homopeptide, along with the presence of these rare motifs, could be responsible for its aggregation phenomena.