Testing bike provided by Favorit1970 (Ivo). Thanks!
Two-speed gearbox with a backpedal brake. On the outside, it looks much like a classic single speed hub, just a bit bigger. Its specialty is lack of cables: just backpedal a little (right before the point where the brake engages) and the gear changes.
First gear is 1 (direct drive), second is 1.38 (overdrive). Besides the backpedal brake version, there is also a disk hub and a brakeless one. The driver accepts sprockets from 13 to 24 teeth and is surprisingly compatible with Czechoslovak Velamos components, making a swap easier. The owner mounted the hub in an Eska folder with 20" wheels, 175 mm cranks and chain transmission ratio of 46/16: one gear for flats, the other for takeoffs and hills - just enough for a city. Having no shifting cables flapping around makes folding easier.
I haven't seen the hub's internals, I just took it for a test ride. Gearing is probably similar to its three-speed cousin: one epicyclic stage with a fixed sun gear. In direct drive, the gear ring is driven via an engaged ratchet. In overdrive, the planet cage is driven and the ratchet clicks around slowly. Every backpedal toggles the gears. The whole thing seems very foolproof: all you can do wrong is to not backpedal far enough and stay in the original gear, or to backpedal too far and brake in addition to shifting. I haven't found any "neutral gears" or non-functional intermediate positions.
The brake is quite sharp before it breaks in, our folder's small and heavily loaded wheel boosted it even more. It will probably become softer after time, but will keep braking pretty well - certainly to the point of locking the rear wheel. Every activation of brake also toggles gears, but you soon learn to keep track of them and shift back if needed.
I have no data about long-term reliability and maintenance so far. Only time will tell...