Standard secular variation curves of the geomagnetic field direction for the last few millennia for different countries in Europe, based mainldy on baked materials discovered in archaeological sites, are reaching sufficient accuracy and reliability that archaeomagnetic dating within this timespan in these areas is becoming feasible now. Orientation errors during sampling and sample preparation can be kept to a minimum and measurement errors of baked materials are in general very small. Nevertheless, even when the secular variation in the site to be dated is similar to that in the reference site, systematic or regular deviations between the remanence vector and geomagnetic field direction in kilns, due to internal and external factors, may result in biased average magnetisation directions and consequently in diverging archaeomagnetic dates. In more or less circular kilns, important non-random deviations of the remanence direction in the walls, in function of the relative azimuth as seen from the centre of the kilns, have been noticed in spite of precise and highly reliable average kiln magnetisation directions. The effect was revealed in the walls of the combustion chambers of roman pottery kilns and of mediaeval brass melting and working kilns, of different shape, lined with refractory bricks. Several hypotheses for the origin of these deviations were examined and anisotropy and/or magnetic refraction are unldikely to be the principal causes. The regular component of these deviations may be responsible for a strongly biased average magnetisation direction when onldy part of the kiln wall is preserved or when sampling is limited to certain parts of it and consequently result in unreliable dates when applying the archaeomagnetic dating method.