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We present the results of the analysis of Type II and anomalous Cepheids using the data from the Kepler K2 mission. The precise light curves of these pulsating variable stars are the key to study the details of their pulsation, such as the period-doubling effect or the presence of additional modes. We applied the Automated Extended Aperture Photometry (autoEAP) to obtain the light curves of the targeted variable stars which were observed. The light curves were Fourier analyzed. We investigated twelve stars observed by the K2 mission, seven Type II and five anomalous Cepheids. Among the Type II Cepheids EPIC 210622262 shows period-doubling, and four stars have modulation present in their light curves which are different from the period-doubling effect. We calculated the high-order Fourier parameters for the short-period Cepheids. We also determined physical parameters by fitting model atmospheres to the spectral energy distributions. The determined distances using the parallaxes measured by the Gaia space telescope have limited precision below 16 mag for these types of pulsating stars, regardless if the inverse method is used or the statistical method to calculate the distances. The BaSTI evolutionary models were compared to the luminosities and effective temperatures. Most of the Type II Cepheids are modeled with low metallicity models, but for a few of them solar-like metallicity ([Fe/H]=0.06) model is required. The anomalous Cepheids are compared to low-metallicity single stellar models. We do not see signs of binarity among our sample stars.