Nanotubes suspended in a fluid medium have been investigated by the electrooptic method. This method is based on measuring the relative changes in the intensity of light transmitted through a suspension of nanotubes with application of an external electric field. The electrooptic effect (difference in these changes for transmitted light plane-polarized along the external field and perpendicularly to it) is analyzed. For aqueous suspensions of Mg3Si2O5(OH)4 nanotubes, the field and relaxation dependences of this effect are investigated. An analysis of the results obtained suggests that nanotubes, even when their concentration in water is low, form strong stable aggregates, which, however, can be elongated and enlarged under long-term action of strong rf fields.