Epoxy nanocomposites with float catalysis-produced CNT felt as a filler were prepared. Parameters such as the curing process, glass transition of epoxynanocomposites, structure and morphology of CNT felt, initial epoxy composition, and epoxy nanocomposites were investigated. The influence of CNT felt on curing process in epoxy nanocomposites with different amounts of curing agent was determined. An exothermic reaction between the curing agent and the surface of CNTs was established. It was found that the structure of epoxy nanocomposites has a high degree of heterogeneity: the presence of fiber-like structures and individualized CNTs is observed together with the regions that are typical for CNTs that are fabricated via a catalytic chemical vapor deposition (CVD). Based on the studies performed, it is possible to predict the production of epoxy nanocomposites with outstanding mechanical and thermophysical properties. In particular, the uncured compositions already obtained in this work can be used for the manufacture of electrically conductive glass and carbon fiber reinforced plastics and functional coatings.