Both are part of a wave of fusion start-ups that aim to succeed where the state has failed.
Nuclear fusion is the process that powers the sun. It involves hydrogen atoms joining to make helium, releasing large amounts of energy but little radiation.
If fusion power can be made to work on Earth it will offer clean power as plentiful as the oceans. However, it has never been made economical.
The most advanced state-funded project, called Iter, in the south of France, has been beset by rising costs and delays.
For many, the old joke about fusion still holds true: for the past 30 years it has always been 30 years away.
Jonathan Carling, chief executive of Tokamak Energy, said that it was time for others to try — and serious investors agree. Tokamak is backed by Legal & General and the British hedge-fund billionaire David Harding. 'Because we are privately funded we can be more agile,' Mr Carling said.
His plan is based on similar ideas to Iter, using superconducting magnets to hold a superheated plasma in position.
However, he said that the devices his company used were smaller and cheaper.
Nick Hawker, co-founder of First Light Fusion, said that his company's project also demonstrated the virtues of the private sector.
He said that it was trying to create a different kind of fusion, firing projectiles at a target to create an instant of huge pressure and heat.
Both say that they can have demonstration devices by 2025.
Tokamak aims to be feeding electricity into the grid by 2030. The private sector has achieved at least one thing, then: fusion has gone from being always 30 years away, to only ten.
HOW DOES FUSION POWER WORK?
Fusion involves placing hydrogen atoms under high heat and pressure until they fuse into helium atoms.
When deuterium and tritium nuclei - which can be found in hydrogen - fuse, they form a helium nucleus, a neutron and a lot of energy.
This is down by heating the fuel to temperatures in excess of 150 million°C, forming a hot plasma.
Strong magnetic fields are used to keep the plasma away from the walls so that it doesn't cool down and lost it energy potential.
These are produced by superconducting coils surrounding the vessel, and by an electrical current driven through the plasma.
For energy production. plasma has to be confined for a sufficiently long period for fusion to occur.