There are disclosed compound of formula I, in which R.sub.1 represents a hydrophobic moiety adapted to occupy the C' channel of human CDId, R.sub.2 represents a hydrophobic moiety adapted to occupy the A' channel of human CDId, such that R.sub.1 fills at least at least 30% of the occupied volume of the C' channel compared to the volume occupied by the terminal nC.sub.14H.sub.29 of the sphingosine chain of .alpha.-galactosylceramide when bound to human CDId and R.sub.2 fills at least 30% of the occupied volume of the A' channel compared to the volume occupied by the terminal nC.sub.25H.sub.51 of the acyl chain of .alpha.-galactosylceramide when bound to human CDId R.sub.3 represents hydrogen or OH, R.sup.a and R.sup.b each represent hydrogen and in addition, when R.sup.3 represents hydrogen, R.sup.a and R.sup.b together may form a single bond, X represents or --CHA(CHOH).sub.nY or --P(.dbd.0)(0.sup.-)0CH.sub.2(CH0H).sub.mY, in which Y represents CHB.sub.1B.sub.2, n represents an integer from 1 to 4, m represents 0 or 1, A arepresents hydrogen, one of B.sub.1 and B.sub.2 represents H, OH or phenyl, and the other represents hydrogen or one of B.sub.1 and B.sub.2 represents hydroxyl and the other represents phenyl, in addition, when n represents 4, then A together with one of B.sub.1 and B.sub.2 together forms a single bond and the other of B.sub.1 and B.sub.2 represents H, OH or OSO.sub.3H and pharmaceutically acceptable salts thereof; the compounds of formula I are indicted for use in the treatment of a virus, microbial infection, parasite, an autoimmune disease, cancer, allergy or asthma ##STR00001##