We present a computer model of avian navigation (homing) based on Kramer's 'Map and Compass' model. The key assumptions are: (1) the navigation environment contains two intersecting gradients, (2) the birds possess senses to measure these gradients, a compass sense, and an internal representation of the gradients, the navigational 'map'. By interpreting the difference in gradient values between home and at the release site with the help of its 'map', the simulated bird determines the homeward course which is then converted with the help of the compass into a heading. After 5 km, the course is recomputed. To assess the simulated birds' performance, we used (1) the mean vector of the initial headings of 50 runs as a measure of initial orientation, and (2) the mean homing efficiency, expressed as the ratio of the direct distance to the length of the route taken. The simulation shows that models of bicoordinate navigation allow successful homing from unknown sites with realistic values for the accuracy of the birds' senses. Irregularities in the navigational factors may lead to initial deviations from the home course and to lower homing efficiencies. Decreasing the accuracy of the compass readings impairs initial orientation and lowers homing efficiency, but the performance remains at a fairly high level for a long time. Decreasing the accuracy of reading gradients leads to a rapid increase in the number of birds getting 'lost', while those that return do so with moderate efficiency. These findings are discussed in view of the average performance of pigeons reflected by release experiments. (c) 2004 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.