We present the current design of the VIsible Multi-Object Spectrograph (VIMOS) and the Near InfraRed Multi-Object Spectrograph (NIRMOS) for the European Southern Observatory Very Large Telescope. The basic scientific requirement is to conduct very deep redshift surveys of large quantities of objects, in a minimum number of nights. The technical specifications are to allow for a large multiplex gain over a wide field, and a high efficiency of the optical train, over the 0.37 to 1.8 micrometer domain. The baseline technical concept is built around 4 channels, covering 4 X 7 X 8 arcmin2 for VIMOS and 4 X 7 X 7 arcmin2 for NIRMOS. Each channel is an imaging spectrograph with a large field adaptation lens, a collimator, grisms or filters, and a F/1.8 camera, coupled to a 2048 X 4096 pixels CCD for VIMOS, and a 20482 HgCdTe Rockwell array for NIRMOS. The unique multiplex gain allows to obtain spectra of up to 840 object simultaneously with VIMOS, and up to 170 with NIRMOS (10 arcsec slits). An integral field spectroscopy mode with more than 6400 fibers coupled to micro-lenses will be available for VIMOS, covering a 1 X 1 arcmin2 field. The VLT-VIRMOS survey of more than 150,000 galaxies is planned down to magnitudes IAB equals 24, coupled to an ultra deep probe to IAB equals 26.