The chemically peculiar (CP) stars HD 98851 and HD 102480 have been discovered to be unusual pulsators during the ``Naini Tal Cape Survey programme to search for pulsational variability in CP stars. Time series photometric and spectroscopic observations of these newly discovered stars are reported here. Fourier analyses of the time series photometry reveal that HD 98851 is pulsating mainly with frequencies 0.208 mHz and 0.103 mHz, and HD 102480 is pulsating with frequencies 0.107 mHz, 0.156 mHz and 0.198 mHz. The frequency identifications are all subject to 1 d$^{-1}$ cycle count ambiguities. We have matched the observed low resolution spectra of HD 98851 and HD 102480 in the range 3500-7400 AA with theoretical synthetic spectra using Kurucz models with solar metallicity and a micro-turbulent velocity 2 km s$^{-1}$. These yield $T_{eff}=7000pm250$ K, log $g=3.5 pm 0.5$ for HD 98851 and $T_{eff} = 6750 pm 250$ K, log $g = 3.0 pm 0.5$ for HD 102480. We determined the equivalent H-line spectral class of these stars to be F1 IV and F3 III/IV, respectively. A comparison of the location of HD 98851 and HD 102480 in the HR diagram with theoretical stellar evolutionary tracks indicates that both stars are about 1-Gyr-old, 2-$M_{odot}$ stars that lie towards the red edge of the $delta$ Sct instability strip. We conclude that HD 98851 and HD 102480 are cool, evolved Am pulsators. The light curves of these pulsating stars have alternating high and low amplitudes, nearly harmonic (or sub-harmonic) period ratios, high pulsational overtones and Am spectral types. This is unusual for both Am and $delta$ Sct pulsators, making these stars interesting objects.
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