In order to produce a nonwoven fabric having elastomeric properties spun filaments (1), consisting preferably (but not essentially) of cellulose material such as cellulose acetate or solvent spun rayon, not in yarn formats, are corrugated or crimped in an overfeed process, as in stuffer box (6), into stabilized three dimensional batts. A proportion of filaments (3) of a thermal memory material, such as modified polyester, in a stretched format are included. The resulting batt is then subjected to controlled hydroentangling and a controlled heat treatment to yield three dimensional nonwoven fabrics with elastomeric properties due to contraction of the stretched filaments. Elastomeric memory material activated to shrink by ultrasonic treatment may be used in place of thermal memory material. The elastomeric properties can be adjusted to suit end-use requirements and applications are envisaged in the medical and hygiene areas.