Alzheimer's dementia is a neurodegenerative disease that affects millions of people worldwide. Early detection of Alzheimer's dementia is crucial for effective treatment and management of the disease. In this paper, we present a cross-lingual approach for detecting Alzheimer's dementia from speech, based on multiple feature streams that capture the individual's speech and conversational interactions. In order to validate the ability of the features to perform well in cross-linguistic scenarios, we evaluate in a zero-shot setup, where the target domain is a language that was not available during training and a few-shot setup, where only limited data is available. Experimental results show that an ensemble system using the features trained on English and evaluated on Greek outperforms the baseline system by 4.4 %. Further experiments show promising zero-shot and few-shot performance on a similar Spanish task.