The multi-level adaptive networks (MLAN) technique is a cross-lingual adaptation framework where a bottleneck (BN) layer in a deep neural network (DNN) trained in a source language is used for producing BN features to be exploited in a second DNN in a target language. We investigate how the correlation (in the sense of phonetic similarity) of the source and target languages and the amount of data of the source language affect the efficiency of the MLAN schemes. We experiment with three different scenarios using, i) French, as a source language uncorrelated to the target language, ii) Ukrainian, as a source language correlated to the target one and finally iii) English as a source language uncorrelated to the target language using a relatively large amount of data in respect to the other two scenarios. In all cases Russian is used as target language. GLOBALPHONE data is used, except for English, where a mixture of LIBRISPEECH, TEDLIUM and AMIDA is available. The results have shown that both of these two factors are important for the MLAN schemes. Specifically, on the one hand, when a modest amount of data from the source language is used, the correlation of the source and target languages is very important. On the other hand, the correlation of the two languages seems to be less important when a relatively large amount of data, from the source language, is used. The best performance in word error rate (WER), was achieved when the English language was used as the source one in the multi-task MLAN scheme, achieving a relative improvement of 9.4% in respect to the baseline DNN model.