This is an announcement for the paper "On kernel theorems for Frechet and DF spaces" by A.G. Smirnov and M.A. Soloviev. Abstract: A convenient technique for calculating completed topological tensor products of functional Frechet or DF spaces is developed. The general construction is applied to proving kernel theorems for a wide class of spaces of smooth and entire analytic functions. Archive classification: Functional Analysis Mathematics Subject Classification: 46A32; 46E10; 46A04 Remarks: 10 pages The source file(s), kernel1.tex: 40782 bytes, is(are) stored in gzipped form as 0501187.gz with size 12kb. The corresponding postcript file has gzipped size 64kb. Submitted from: smirnov at lpi.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0501187 or http://arXiv.org/abs/math.FA/0501187 or by email in unzipped form by transmitting an empty message with subject line uget 0501187 or in gzipped form by using subject line get 0501187 to: math at arXiv.org.