The (1)Sigma(+) and (3)Sigma(+) stares of NaH dissociating into the 3s-5s states of Na and the (1)Sigma(+) and (3)Sigma(+) states of KH dissociating into the 4s-6p states of K are calculated using the effective core potential with the core polarization potential and the configuration interactions. Apart from ionic-neutral avoided crossings in cascade for the singlet states and neutral-neutral avoided crossings in both singlet and triplet states, all these states also show the undulating potential curves discovered recently: Phys. Rev. A 59 (1999) 1178-1186. The apparently complex potential curves are analyzed in this work.