Limestone samples from the Cambro-Ordovician Durness Group were crushed, acid-digested and searched for evidence of micrometeorites. Eleven melted micrometeorites were extracted from the magnetic fraction of samples from the Balnakeil and Croisaphuill formations near the top of the group. Other formations in the Durness Group did not yield micrometeorites. Only melted spherules with a distinctive dendroidal crystalline structure (I-type cosmic spherules) were accepted as definite micrometeorites. They represent a flux of micrometeorites one to two orders of magnitude greater than at present. The micrometeorite-bearing formations are of Arenig age, coincident with the onset of an enhanced flux of extraterrestrial material identified by the occurrence of fossil meteorites in Sweden.