Cross-lingual adaptation is a special case of domain adaptation and refers to the transfer of classification knowledge between two languages. In this article we describe an extension of Structural Correspondence Learning (SCL), a recently proposed algorithm for domain adaptation, for cross-lingual adaptation in the context of text classification. The proposed method uses unlabeled documents from both languages, along with a word translation oracle, to induce a cross-lingual representation that enables the transfer of classification knowledge from the source to the target language. The main advantages of this method over existing methods are resource efficiency and task specificity. We conduct experiments in the area of cross-language topic and sentiment classification involving English as source language and German, French, and Japanese as target languages. The results show a significant improvement of the proposed method over a machine translation baseline, reducing the relative error due to cross-lingual adaptation by an average of 30% (topic classification) and 59% (sentiment classification). We further report on empirical analyses that reveal insights into the use of unlabeled data, the sensitivity with respect to important hyperparameters, and the nature of the induced cross-lingual word correspondences.