Aqueous solutions of a copolymer derivative of a polyacrylamide showed very interesting behavior, that in which the system evolves from one kind of double criticality (pressure-hypercritical point) to another (temperature-hypercritical point) as polymer molecular weight decreases. While in the neighboring region of the former point one expects a change from contraction to expansion upon mixing with increasing pressure; in the latter, mixing should be accompanied by a change in the sign of the excess enthalpy as temperature increases. L-L equilibria studies were performed in a wide range of (T, p) experimental conditions (300 < T/K < 460, 0 < p/bar < 700). Poly(N-isopropylacrylamide), usually called PNIPAAM, and its copolymer derivative poly(N-isopropylacrylamide/1-deoxy-1-methacrylamido-D-glucitol), herein referred to as CP, were investigated for several chain lengths and compositions. An He/Ne laser light scattering technique was used for the determination of cloud-point (T, p, x) conditions. The experimental results were used to assist in the determination of computed values at temperatures beyond experimental accessibility, which are obtained by the application of a modified Flory-Huggins model. The model also estimates the excess properties of these solutions. Because of the intrinsic self-associating nature of these systems, all studied solutions show a lower critical solution temperature (LCST). Both modeling results and H/D isotope substitution effects suggest also the existence of upper critical solution temperatures (UCST) and therefore closed-loop-type phase diagrams. However, these upper-temperature branches are experimentally inaccessible. Pressure effects are particularly interesting. For a low-MW CP, experimental data display a tendency toward a reentrant T-p locus, which supports the conjecture that these systems are inherently of the closed-loop type. In the cases of PNIPAAMs and high-MW CPs, the T-p isopleths show extrema. The copolymer aqueous solutions under study in this work model a single chemical system where pressure-hypercritical behavior evolves to a temperature-hypercritical one as the chain length decreases.