Originally Posted by
dropspace
it would not be advisable to use QR axles. You are likely to rip the wheel right out of the dropout because of the stresses a fixed gear puts on them.
solid axles with track nuts, do it for the children
The stresses on the wheel of a fixed gear bike are no different than those on a freewheel bike, but modern quick releases in general are not strong enough to secure a wheel in a horizontal dropout.
Quick releases *were* allowed on the track as recently as the 1960s; they were banned not because of slippage concerns, but because of concern that other riders' wheels could snag on the lever, either opening the lever or causing one or both bikes to crash. This is not pretty on the track.