Meet Atlas, a humanoid robot capable of crossing rough terrain and maintaining its balance on one leg even when hit from the side.
And WildCat, the four-legged robot that can gallop untethered at up to 16mph (26km/h).
These are the latest creations of Boston Dynamics, a US robotics company part-funded by the Defense Advanced Research Projects Agency (Darpa).
The robots are part of Darpa's Maximum Mobility and Manipulation programme.
Darpa says such robots "hold great promise for amplifying human effectiveness in defence operations".
Referring to Atlas's ability to remain balanced despite being hit by a lateral weight, Noel Sharkey, professor of Artificial Intelligence and Robotics at the University of Sheffield, told the BBC: "This is an astonishing achievement... quite a remarkable feat."
This version of Atlas is one of seven humanoid robots Boston Dynamics is developing in response to the Darpa Robotics Challenge.
In December, competing robots will be set eight tasks to test their potential for use in emergency-response situations, including crossing uneven ground, using power tools and driving a rescue vehicle.
Darpa wants to improve the manoeuvrability and controllability of such robots while reducing manufacturing costs.
WildCat can bound, gallop and turn, mimicking the movements of quadruped animals. It is powered by an internal combustion engine.
"It is a shame that such technology is not being developed with other research funding," said Prof Sharkey, who is also chair of the International Committee for Robot Arms Control.
"We do not know what military purpose it will serve but certainly it is a step towards a high-speed ground robot that could be weaponised to hunt and kill."
The video shows WildCat performing on a flat surface, but Prof Sharkey said: "It would be good to see how well it could perform in a muddy field."
Last year, Boston Dynamics' Cheetah robot reached a sprint speed of 28.3mph tethered to a treadmill.
Geoff Pegman, managing director of RURobots, told the BBC: "Robotics has been making important strides in recent years, and these are a couple of demonstrations of the technology moving forward.
"However, their application may be limited to areas such as defence and, maybe specialised construction or demolition tasks.
"In other applications there are more efficient ways of achieving the mobility more cost effectively."