NMR rotational correlation times tau(2R) for heavy-water molecules (D2O) were measured by the integrated capillary method in pure water (tau(2R)(0)) and dilute aqueous solutions of benzene (23 mM) and phenol (55 mM) over a wide range of temperatures including the supercooling range down to -18 degrees C. The B-tau coefficient defined by B-tau = (partial derivative tau(2R)/partial derivative c)tau(2R)(0) (c, concentration) is positive and negative for benzene and phenol, respectively, and its magnitude increases with the decrease in temperature for both solutes. Benzene, an apolar molecule, is classified as a structure maker and phenol, a polar molecule, as a breaker. They are more clearly distinguished in the supercooled region. The correlation time for the shell water molecules, which is shown to be expressed by tau(2R)(shell) = [l + (55/Z)B-tau]tau(2R)(0) (Z, hydration number), is 4.1 times as large as the tau(2R)(0) value (14.6 ps) in supercooled aqueous solution of benzene (Z = similar to 23) at -18 degrees C. This means that the hydrophobic hydration of benzene is associated with a remarkable rotational slowdown or increase in the local viscosity.