A fast curable non-isocyanate-based polyurethane- and polyurethane-epoxy network nanocomposite polymeric compositions are derived upon crosslinking a mixture comprising of natural or modified nano-clay [ionic phyllosilicate] with platelet thickness in the scale of Å (˜1 nm) and aspect ratio (length/thickness) higher than 10 (nm)] preferably natural or modified montmorillonite with either a monomer(s) or oligomer(s) bearing at least one cyclocarbonate group or a mixture of the latter with an epoxy resin, with a hardener, which is a monomer or oligomer or mixtures therefrom, bearing primary and/or secondary amino groups. The use of the nanoclays reduces the gel time and increases the adhesion of the cured polyurethane and polyurethane/epoxy hybrid and also reduces its water absorption.