gaeronf, I'm going to risk getting myself in trouble here. First, I believe it is most times very difficult to identify a critter by a photo; however, I will point out some characteristics of the flies you photographed and see what we've got.
Your first photo is definitely a two-tailed critter. Second, it is a male as can be determined by its large eyes. Third, the secondary wing is fairly large.
By a process of elimination we can rule out a Hendrickson spinner. Hendricksons are a three-tailed critter. We can also rule out a Baetis, or BWO, spinner, since Baetis has a very small, elongated secondary wing.
Now, here's where it gets tricky. You didn't give us any indication of size and that's very important. Without that info it becomes even more difficult. My guess - and that's all it is - is a Quill Gordon spinner, male. That would mean your critter was about a size 14 equivalent?
As for the photo of the dun it, too, is a male with those large eyes. I think I see only two tails and I think I see a very small elongated secondary wing. These are characteristic of a Baetis, or BWO. Again, you gave us no indication of size. Again, I'm guessing. That would mean your critter was about a size 18 or 20 equivalent?