Wide-angle X-ray scattering and 2 9 Si NMR have been employed to investigate the medium-range structure of xK 2 O-(1-x)SiO 2 glasses, with x varying in the limits 5%<x<35%. The diffractograms show a first sharp diffraction peak (FSDP) in the 1.4A - 1 <q<2.2A - 1 range. The peaks broaden below x=20%, and at the lowest K 2 O fraction, a bimodal line shape is found. This broadening is interpreted in terms of phase separation at low K 2 O fraction. The NMR spectra consist of several (usually three) Gaussian components assigned to the different Q species (SiO 4 tetrahedra with different connectivity) present. All three components are uniformly deshielded as K 2 O is incorporated into the structure. The fraction of non-bridging oxygens (NBOs) derived from the distribution of Q species matches the value obtained from the overall composition, except for the x=17.41% sample, again indicating phase-separation at x<20%. The inhomogeneities found by WAXS and NMR in the xK 2 O-(1-x)SiO 2 glasses are interpreted in terms of broken bond-bending constraints at the NBOs. Constraint theory assigns the critical concentration for glass forming at x c =20%, which may explain the tendency of the glasses to phase-separate at concentrations below x c .