All internal organs are asymmetric along the left–right axis. Here we report a genetic screen to discover mutations which perturb organ laterality. Our particular focus is upon whether, and how, organs are linked to each other as they achieve their laterally asymmetric positions. We generated mutations by ENU mutagenesis and examined F3 progeny using a cocktail of probes that reveal early primordia of heart, gut, liver and pancreas. From the 750 genomes examined, we isolated seven recessive mutations which affect the earliest left–right positioning of one or all of the organs. None of these mutations caused discernable defects elsewhere in the embryo at the stages examined. This is in contrast to those mutations we reported previously (Chen et al., 1997) which, along with left–right abnormalities, cause marked perturbation in gastrulation, body form or midline structures. We find that the mutations can be classified on the basis of whether they perturb relationships among organ laterality. In Class 1 mutations, none of the organs manifest any left–right asymmetry. The heart does not jog to the left and normally leftpredominant BMP4 in the early heart tube remains symmetric. The gut tends to remain midline. There frequently is a remarkable bilateral duplication of liver and pancreas. Embryos with Class 2 mutations have organotypic asymmetry but, in any given embryo, organ positions can be normal, reversed or randomized. Class 3 reveals a hitherto unsuspected gene that selectively affects laterality of heart. We find that visceral organ positions are predicted by the direction of the preceding cardiac jog. We interpret this as suggesting that normally there is linkage between cardiac and visceral organ laterality. Class 1 mutations, we suggest, effectively remove the global laterality signals, with the consequence that organ positions are effectively symmetrical. Embryos with Class 2 mutations do manifest linkage among organs, but it may be reversed, suggesting that the global signals may be present but incorrectly orientated in some of the embryos. That laterality decisions of organs may be independently perturbed, as in the Class 3 mutation, indicates that there are distinctive pathways for reception and organotypic interpretation of the global signals.