Cross-lingual speaker adaptation for speech synthesis has many applications, such as use in speech-to-speech translation systems. Here, we focus on cross-lingual adaptation for statistical speech synthesis systems using limited adaptation data. To that end, we propose two eigenvoice adaptation approaches exploiting a bilingual Turkish-English speech database that we collected. In one approach, eigenvoice weights extracted using Turkish adaptation data and Turkish voice models are transformed into the eigenvoice weights for the English voice models using linear regression. Weighting the samples depending on the distance of reference speakers to target speakers during linear regression was found to improve the performance. Moreover, importance weighting the elements of the eigenvectors during regression further improved the performance. The second approach proposed here is speaker-specific state-mapping, which performed significantly better than the baseline state-mapping algorithm both in objective and subjective tests. Performance of the proposed state mapping algorithm was further improved when it was used with the intralingual eigenvoice approach instead of the linear-regression based algorithms used in the baseline system.