[1] His work has focused on ultra-condensed matter at extreme pressures, densities and temperatures achieved by fast dynamic compression.

He is most well-known for the first experimental observation of a metallic phase of dense hydrogen, a material predicted to exist by Eugene Wigner and Hillard Bell Huntington in 1935.

[2] Nellis has been President of the International Association for the Advancement of High Pressure Science and Technology (AIRAPT) and Chairman of the American Physical Society (APS) Topical Group on Shock Compression of Condensed Matter.

[1] His Ph.D. thesis research included measurements of electrical and thermal conductivities of single crystals of the Rare Earth elements Gadolinium, Terbium and Holmium in the Ames National Laboratory at Iowa State.

[7] Following graduate school, Nellis was a postdoctoral researcher in the Materials Science Division of Argonne National Laboratory (ANL), where he measured electrical and magnetic properties of ordered and disordered alloys of the Actinide elements Plutonium, Neptunium and Uranium mixed with non-magnetic Transition Metals.

In 1973, he left Monmouth to join Lawrence Livermore National Laboratory (LNLL), where he performed computational simulations of condensed matter under dynamic compression driven by shock waves generated with high explosives.

[9] In 1976, Nellis moved within LLNL to the High-Dynamic-Pressure Experimental Group, in which he measured properties of approximately 30 cryogenic liquids and solids compressed dynamically to pressures in the range 20-500 GPa with associated temperatures up to as much as several 1000 Kelvins.

[9] Nellis is most well-known for the first experimental observation of a metallic phase of dense hydrogen,[10][11] a material predicted to exist by Wigner and Huntington in 1935.