Phase diagrams with very flat LCST phase separation line for aqueous poly(N-isopropyl-acrylamide) (PNIPAM) solutions are theoretically derived on the basis of sequential hydrogen bond formation between polymer chains and water molecules (cooperative hydration) and compared with experimental spinodal curves. The two-phase region systematically changes its shape with the cooperativity parameter σ, and the spinodals turned out to be almost independent of the polymer molecular weight for strongly cooperative hydration (small σ) as observed in PNIPAM solutions. Hydration takes place sharply within a very narrow temperature region. The number of hydrogen-bonded water molecules on a chain is calculated as a function of the temperature and the polymer concentration.