Human exploration of the Solar System is one of the most challenging objectives included in the space programs of the most important space agencies in the world. Since the Apollo program, and especially with the construction and operation of the International Space Station, extravehicular activities (EVA) have become an important part of space exploration. This article presents a soft hand exoskeleton designed to address one of the problems that astronauts face during spacewalks: hand fatigue caused by the pressurized EVA gloves. This device will reduce the stiffness of the spacesuit glove by counteracting the force exerted by the pressurized glove. To this end, the system makes use of a set of six flexible actuators, which use a shape memory alloy (SMA) wire as the actuating element. SMAs have been chosen because some of their features, such as low volume and high force-to-weight ratio, make them a suitable choice taking into account the constraints imposed by the use of the device in a spacesuit. Besides describing the different mechanical and electronic subsystems that compose the exoskeleton, this article presents a preliminary assessment of the device; several tests to characterize its nominal operation have been carried out, as well as position and force control tests to study its controllability and evaluate its suitability as a force assistive device.