How K(+) channels are able to conduct certain cations yet not others remains an important but unresolved question. The recent elucidation of the structure of NaK, an ion channel that conducts both Na(+) and K(+) ions, offers an opportunity to test the various hypotheses that have been put forward to explain the selectivity of K(+) ion channels. We test the snug-fit, field-strength, and over-coordination hypotheses by comparing their predictions to the results of classical molecular dynamics simulations of the K(+) selective channel KcsA and the less selective channel NaK embedded in lipid bilayers. Our results are incompatible with the so-called strong variant of the snug-fit hypothesis but are consistent with the over-coordination hypothesis and neither confirm nor refute the field-strength hypothesis. We also find that the ions and waters in the NaK selectivity filter unexpectedly move to a new conformation in seven K(+) simulations: the two K(+) ions rapidly move from site S4 to S2 and from the cavity to S4. At the same time, the selectivity filter narrows around sites S1 and S2 and the carbonyl oxygen atoms rotate 20 degrees -40 degrees inwards toward the ion. These motions diminish the large structural differences between the crystallographic structures of the selectivity filters of NaK and KcsA and appear to allow the binding of ions to S2 of NaK at physiological temperature.