The available data on the enthalpy relaxation rate, dH(m)/dt, and specific heat, C-p.m. of water in 1.8 nm pores of MCM-41 are interpreted by considering surface interactions and the number of H2O molecules available to crystallize or vitrify. Out of a maximum of five H2O molecules in a close-packing along the 1.8 nm diameter pore, at least two would form an uncrystallizable shell bonded to the silica wall and three would remain as a 1.1 nm diameter nanocore, which is too small for nucleation of the usual ice crystals. The dH/dt features observed in the temperature range of 90-130 K and 125-175 K show kinetic unfreezing or glass-softening characteristics. The first is attributed to the reorientation of H2O in the nanoshell with little change in their center of mass position and the second to the change in the population of bonds between water and silica surface. The third dH(m)/dt feature observed in the 180-230 K range is inconsistent with kinetic unfreezing or glass-softening and is attributed to the formation and melting of distorted ice-like unit cells with or without the growth- and stacking-faults that remain at equilibrium with the melt. The large increase in C-p.m. at T near 210 K is attributed to the latent heat of their "melting", as occurs on premelting of fine-grain ice and other solids. Data on the pore size dependence qualitatively support this interpretation. Structure of the water in nanopores depends on the pore size, and its properties differ from those of bulk water. (C) 2009 Elsevier B.V. All rights reserved.