This paper, first of a series, maps out the changes in molecular orientation occurring when doubly-oriented polyethylene is heat relaxed as a preliminary to further work on the relation of molecular orientation and crystalline texture. While earlier investigations have dealt with individual aspects of this field, the present results have now brought the previous, in some respects diverging views, into a single, unified scheme. Drawing followed by rolling produces a twinned, double texture which has been shown to result from a single texture (single crystal analogue) present under pressure, in agreement with an earlier hypothesis. The same single crystal analogue is produced by slight annealing. Further annealing leads to progressive molecular tilt around the b crystal axis and finally to a texture which is the macroscopic analogue of a solution grown crystal platelet. Beyond this stage, randomisation around b sets in, resulting in a texture analogue of a spherulitic fibril (Point's fibre “N”). Some orientation in the non-crystalline position of the material is also indicated, which, however, decays faster than that of the crystals.