Mon.Not.Roy.Astron.Soc.326:147,2001 We compute the redshift space power spectrum of two X-ray cluster samples: the X-ray Brightest Abell Cluster Sample (XBACS) and the Brightest Cluster Sample (BCS) using the method developed by Feldman, Kaiser & Peacock. The power spectrums derived for these samples are in agreement with determinations of other optical and X-ray cluster samples. For XBACS we find the largest power spectrum amplitude expected given the high richness of this sample ($R \ge 2$). In the range $0.05 \uk < k < 0.4 \uk$ the power spectrum shows a power law behavior $P(k)\propto k^{n}$ with an index $n\simeq-1.2$. In a similar range $0.04 \uk < k < 0.3 \uk $ BCS power spectrum has a smaller amplitude with index $n\simeq-1.0$. We do not find significant evidence for a peak at $k \simeq 0.05 \uk$ suggesting that claims such of feature detections in some cluster samples could relay on artificial inhomogeneities of the data. We compare our results with power spectrum predictions derived by Moscardini et al. within current cosmological models (LCDM and OCDM). For XBACS we find that both models underestimate the amplitude of the power spectrum but for BCS there is reasonably good agreement at $k\gsim 0.03 \uk$ for both models.