Recent evidence suggests division of labor in phonological analysis underlying speech recognition. Adults and children appear to decompose the speech stream into phoneme‐relevant information and into syllable stress. Here we investigate whether both speech processing streams develop from a common path in infancy, or whether there are two separate streams from early on. We presented stressed and unstressed syllables (spoken primes) followed by initially stressed early learned disyllabic German words (spoken targets). Stress overlap and phoneme overlap between the primes and the initial syllable of the targets varied orthogonally. We tested infants 3, 6 and 9 months after birth. Event‐related potentials (ERPs) revealed stress priming without phoneme priming in the 3‐month‐olds; phoneme priming without stress priming in the 6‐month‐olds; and phoneme priming, stress priming as well as an interaction of both in 9‐month‐olds. In general the present findings reveal that infants start with separate processing streams related to syllable stress and to phoneme‐relevant information; and that they need to learn to merge both aspects of speech processing. In particular the present results suggest (i) that phoneme‐free prosodic processing dominates in early infancy; (ii) that prosody‐free phoneme processing dominates in middle infancy; and (iii) that both types of processing are operating in parallel and can be merged in late infancy. Using word onset priming, we tested whether infants represent phonemes and syllable stress of frequently appearing words. Event‐related potentials revealed that 3‐month‐olds focus on syllable stress, while 6‐month‐olds focus on phonemes. Only 9‐month‐olds combined both aspects of the speech signal.