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Three chemical groups of primary “silicate” spheres <30 µm in diameter of cometary origin were collected in the lower stratosphere between 1981 May and 1994 July. The “silicate” sphere abundances represent an annual background from contributions by sporadic meteor and weak annual meteor shower activities. During two collection periods, from 06/22 until 08/18, 1983 (U2015), and from 09/15–12/15, 1981 (W7027/7029), a higher number of spheres was collected compared to other periods of the year represented by the other collectors studied here. This study links two different data sets, viz. the NASSA/JSC Cosmic Dust Catalogs and peak activities of annual meteor showers, and identified high-velocity cometary sources for collected stratospheric “silicate” spheres. The majority of spheres on flag U2015 may originate from comet P/Swift-Tuttle (Perseids), while the majority of spheres on flags W7027/7029 could be from comet P/Halley (Orionids) or comet P/Tempel-Tuttle (Leonids). Variations in relative proportions of the Mg,Si,Ca ± Al, Mg,Si ± Fe and Al, Si,Ca spheres may offer a hint of chemical differences among high-velocity comets. Proof for the findings reported here might be obtained by targeted cosmic dust collections in the lower stratosphere including periods of meteor shower and storm activity.