An anti-backlash nut assembly for translational movement along the axis of a leadscrew in response to rotational movement of the nut assembly relative to the leadscrew. The nut assembly comprises (i) a primary nut having an internal thread which mates with an external thread on the leadscrew; (ii) a secondary nut having an internal thread which mates with the external thread on the leadscrew, the secondary nut being capable of rotational movement about the leadscrew independent of the primary nut; (iii) a spring disposed intermediate the primary nut and the secondary nut; and (iv) a housing connected to the said primary nut which surrounds the spring and the secondary nut, for imparting rotational movement applied thereto simultaneously to the primary nut and the secondary nut. In a second embodiment, the nut assembly comprises (i) a primary nut having an internal thread which mates with an external thread on the leadscrew; (ii) a preload member having an internal thread which mates with the external thread on the leadscrew, the secondary nut being capable of rotational movement about the leadscrew independent of the primary nut; (iii) a spring disposed intermediate the preload member and an adjustment member; and (iv) an adjustment member connected to the housing and having a bore for insertion of the leadscrew therethrough; and (v) a housing connected to the primary nut which surrounds the spring, the preload member and the adjustment member, for imparting rotational movement applied thereto simultaneously to the primary nut and the preload member. The adjustment member capable of rotating about the leadscrew for adjusting the preload of the spring while the nut assembly is mounted on the leadscrew.