Could it be the speaking in tongues?
Romans 8:26
ESV - 26 Likewise the Spirit helps us in our weakness. For we do not know what to pray for as we ought, but the Spirit himself intercedes for us with groanings too deep for words.
Rebekka, good question! "And they were all filled with the Holy Ghost, and began to speak with other tongues, as the Spirit gave them utterance." This verse in Acts 2:4 tells us that speaking in tongues is utterance. Scripture also teaches us that the Spirit is praying, not us, with groanings that cannot be uttered (here in Romans 8:26). Tongues is utterance. Groanings is not utterance. So, no, the groaning referred to in Romans 8:26 could not be the speaking in tongues!