Prominent geophysical anomalies of several km extent were noted in the vicinity of the farm Stardalur in southwestern Iceland in a gravity survey published in 1954, as well as in a 1968 total-field aeromagnetic survey published in 1970, and a seismic refraction study of the crust published in 1971. Further low-altitude and ground magnetic surveys were conducted around Stardalur in 1969–1973, and an exploratory hole was drilled to 200 m depth in 1969–1970 at the site of a very distinct peak in the ground anomaly. Various studies were carried out on a core (to 143 m depth) and on cuttings recovered by the drilling. From 41 m depth down, this material consisted of altered olivine tholeiite lava flows, with a mean remanent magnetization intensity of the order of 15 times the average for Icelandic Tertiary lavas. Modelling of the anomaly peak, which was found to reach at least 27μT above the main geomagnetic field intensity of 52μT, indicated that the lava flows formed a body of dimensions about 200 by 600 m striking NE to NNE, inside a caldera structure. This structure probably dates from a normal-polarity subchron around 2 m.y. ago during the Matuyama geomagnetic chron. Further studies on samples from the Stardalur drill core revealed the presence of quite pure and slightly cation-deficient magnetite, whose percentage in the lavas is more than twice the average for Tertiary basalts in Iceland. The magnetite has largely been formed by exsolution from titanomagnetite, but it is also present in small grains which have separated from olivine. A very minor proportion of the magnetite may be of single-domain size, and it appears not to be a decisive factor in the bulk magnetic properties of the lavas. For instance, the natural remanence is much less resistant to alternating-field demagnetization than could be expected for single-domain grains. It is not certain whether it is a primary thermal remanence or of secondary origin, although the former seems more plausible. In agreement with the conclusions of previous researchers, it appears likely that the strong magnetization is due to a chance combination of circumstances (such as high magnetite content, high oxidation state, and strong ambient field) rather than to some unique phenomenon. In this paper, a new ground magnetic survey at Stardalur is presented, along with a simple model of the source of the main anomaly peak. The geological reasons for the creation of that source remain unknown, but comparisons are made with a magnetic anomaly at Hvanneyri in western Iceland which has similarities with the Stardalur anomaly.