The behavior of model associative polymers (MAPs), hydrophobically modified poly(ethylene oxide) of molecular weight 2000 to 6000 g/mol, in aqueous solution has been studied by turbidimetry, differential scanning calorimetry (DSC), and small-angle X-ray scattering (SAXS) measurements. For the polymer of the lowest molecular weight, 2000 g/mol, a complete schematic phase diagram has been sketched. The turbidimetric and DSC studies show that two two-phase regions appear : (1) at low polymer concentration, upon heating above the temperature traditionally called the cloud-point temperature (CPT), and (2) at high polymer content, upon cooling below the crystallisation temperature of the PEO chains. This low molecular weight polymer exhibits a large region of liquid crystallinity which is stable from room temperature up to approximately 60 degrees C. The SAXS measurements of the present work show that this cubic structure is either a simple cubic structure sc or a body centered cubic structure bcc, but geometrical considerations favor the later structure. The distance between the lattice points is compatible with the end-to-end distance of the PEO chains plus the diameter of the hydrophobic microdomain. The radii of the domains which are assumed to be spherical are very close to those obtained for diblock low molecular weight surfactants of C(12)EO(y) type in micellar or mesomorphic phases. At higher concentrations, a lamellar phase is formed in equilibrium with the cubic phase. This phase is of the same type as the lamellar phase formed by unmodified polyethylene oxide. Some additional information about the influence of the molecular weight of the PEO chains on the limits between the different regions of the diagrams and on the cubic phase characteristics is presented.