During the common flight of STS-76 and Mir Linda Godwin and Michael Clifford performed an EVA on March 27, 1996 (6h 02m) to attach the Mir Environmental Effects Payload (MEEP), including 4 different experiments, onto handrails located on the Mir Docking Module. The spacewalk was the first ever performed from the docked Space Shuttle and Mir complex.
The Simplified Aid For EVA Rescue (SAFER), first test-flown on shuttle mission STS-64 in September 1994, were worn by Linda Godwin and Michael Clifford and were used only for a contingency. Spacewalking equipment to be evaluated consisted of several new tether designs with hooks that can be attached to both space shuttle handrails and to Mir space station handrails. Normal space shuttle tether hooks are not large enough to be connected to the Mir handrails. A U.S. camera mounted on the exterior of the Mir docking module, used during STS-74 to align the module as it was permanently docked to the Mir, also were removed by the spacewalkers and returned to Earth for reuse.
Prior to beginning the spacewalk, the hatches of both Atlantis and the Mir were closed at the docking mechanism. A hatch at the end of the shuttle tunnel adapter also was closed, allowing only the airlock and tunnel to be depressurized. All of the shuttle crew members were in Atlantis' crew cabin for the duration of the spacewalk, and all Mir crew members, including Mir-21 crewmember Shannon Lucid, were aboard the Mir.
Linda Godwin and Michael Clifford removed the four MEEP experiment containers from their stowed positions along the right and left sides of Atlantis' cargo bay. Each experiment container was attached to handrails on the exterior of the docking module using special clamps installed by Linda Godwin and Michael Clifford. After each experiment package was clamped to the appropriate module handrails, the spacewalkers unfolded the packages to expose the experiment panels.
The tools evaluated were called Common US/Russian EVA tools and included safety tethers with larger hooks to allow attachment to the Mir's exterior handrails and a new foot restraint also designed to allow attachment to the Mir fixtures.
To remove the Docking Module television camera, the spacewalkers used cable cutters to sever the cable connecting the camera and then turned a knob that released the camera's mounting. The camera was tethered and taken aboard Atlantis.

During five days of docked operations, about 1,500 pounds (680 kilograms) of water and two tons of scientific equipment, logistical material and resupply items transferred to Mir; experiment samples and miscellaneous equipment brought over to orbiter. In Biorack, 11 separate scientific investigations were conducted. Study topics included effect of microgravity and cosmic radiation on plants, tissues, cells, bacteria and insects and effects of microgravity on bone loss. Also transferred to station were Mir Glovebox Stowage (MGBX) equipment to replenish glovebox already on station; Queen's University Experiment in Liquid Diffusion (QUELD) flown in orbiter middeck locker; and High Temperature Liquid Phase Sintering (LPS) experiment.

Payload bay configuration included Orbiter Docking System in forward area and SPACEHAB single module toward the aft. STS-76 began a series of Shuttle-Mir missions that carried a SPACEHAB module onboard. Over the course of these missions, SPACEHAB modules carried a mix of supplies and scientific equipment to and from Mir.