  The hot $\gamma$~Doradus stars have multiple low frequencies characteristic
of $\gamma$~Dor or SPB variables, but are located between the red edge of the
SPB and the blue edge of the $\gamma$~Dor instability strips where all
low-frequency modes are stable in current models of these stars. Though
$\delta$~Sct stars also have low frequencies, there is no sign of high
frequencies in hot $\gamma$~Dor stars. We obtained spectra to refine the
locations of some of these stars in the H-R diagram and conclude that these
are, indeed, anomalous pulsating stars. The Maia variables have multiple high
frequencies characteristic of $\beta$~Cep and $\delta$~Sct stars, but lie
between the red edge of the $\beta$~Cep and the blue edge of the $\delta$~Sct
instability strips. We compile a list of all Maia candidates and obtain spectra
of two of these stars. Again, it seems likely that these are anomalous
pulsating stars which are currently not understood.
