In 1985, Edgren et al. proposed a modified version of the competition
theory to explain the interaction of sensitizers and protectors with t
arget molecules damaged by radiation, which was designated the 'X' mod
el. This model incorporates concepts which have been considered previo
usly, namely that a type of radiation damage exists which cannot be ch
emically repaired, and that cells may contain a naturally occurring se
nsitizer. The model leads to testable predictions, such as, e.g. the c
rossing of 'K curves' when the level of protection is varied. It can o
nly be applied to the immediate effects of radiation, i.e. before enzy
matic reactions play a part. The present paper is a summary of work ca
rried out since 1985 to test the predictions of the 'X' model and an e
xposition of the related algebra.