We report a spectroscopic hyperfine structure study of the (YbF)-Yb-174 molecule in the excited states A (2)Pi(1/2) (v=0), A (2)Pi(1/2) (v=1), and [18.6]0.5(v=0). The fluorine hyperfine interaction constant A(parallel to) in each state is, respectively, -1.6+/-2 MHz, 48.8+/-3 MHz, and 63.3+/-3 MHz. The corresponding values of A(perpendicular to) are 4.6+/-1 MHz, -24.7+/-1 MHz, and -31.9+/-1 MHz. The very small hyperfine interaction characteristic of A (2)Pi(1/2) (v=0) is not seen in A (2)Pi(1/2) (v=1) because this state is strongly mixed with [18.6]0.5(v=0). Analysis of our results shows that the lower-lying of the two mixed states is predominantly of [18.6]0.5(v=0) character, not A (2)Pi(1/2) (v=1) as had previously been thought. The deperturbed hyperfine constants for [18.6]0.5 are A(parallel to)=114+/-5 MHz and A(perpendicular to)=-61+/-2 MHz, comparable with those in the X state and much stronger than in the unperturbed A (2)Pi(1/2) state. This supports the view that the state [18.6]0.5 is of 4f(13)6s(2) character.