What size are the nuts holding the front wheel? I am trying to install a front wheel on a bike - the axle of the wheel is threaded, but I'm having trouble finding out what size thread it is, and what nut can go on this. The size of the thread on the axle is the same as an 8 mm screw, but a standard M8 nut (with 13 mm hex) does not fit on it. Do bikes have some special kind of nut there?

If I look at the thread, and at a standard M8 screw, the thread on the bike axle is a bit more dense then on the screw, but I am not aware of existence of two kinds of M8 nuts, so far every M8 nut I've seen fits every M8 screw.
Park Tool list a number of common sizes. 


  3/8 inch x 24 tpi Some solid axle bikes, including coaster brake
  3/8 inch x 26 tpi Solid rear axle
  10mm x 1mm    Most quick release rear axles
  10mm x 26 tpi Rear axle, quick release, Campganolo®


Note that the difference between 24 and 26 tpi is small and can be subtle, meaning that if you're using a spanner to do the nut up you can wreck the nut without really noticing that anything is wrong. The symptom is often that the nut strips before ever becoming tight. To avoid this put the nut on by hand until it is right over the axle. If it still spins freely it is the right thread pitch.

Less commonly you will find 12mm or 14mm axles, often on load bikes and Asian or African bikes, and some mountain bikes. But those are fairly obvious. Some older front axles were 9mm or even 8mm, and they bend easily. It's sometimes possible to replace a 9mm axle with a 10mm one, depending on the bearing cups you have available.