HYDROXYALKYL polyhydric alcohol ether compounds of the general formulae (I) and (II) have excellent thickening effect and stability at low temperature, are useful as a thickening agent usable for the preparation of liquid detergents, can be produced by a condensation reaction of 1,2-epoxyalkanes of the formula (III) with aliphatic diols of the formula (IV), and are usable for the production of liquid detergent compositions, together with various surfactants (except for cationic surfactants), particularly sulfur atom-containing anionic surfactants or dipolar-ionic surfactants. 1