There is a possibility that small traces of long-lived superheavy elements (Z⩾104) still exist in nature. An ultrasensitive search for such superheavy elements has been conducted at the Maier-Leibnitz Laboratory in Garching (Germany) by means of accelerator mass spectrometry. A sample of raw platinum has been scanned for 13 different masses in the range 292⩽A⩽310. The masses A=292 and 298 were scanned in pure osmium and pure lead fluoride, respectively. For each mass, several hours of background-free data were recorded. Since no events could be attributed to superheavy elements, upper limits on their abundances in the sample materials on the order of 10−14–10−16 were established.