Although much effort has been put into speech understanding systems there still exists a rather wide gap between acoustic recognition and linguistic interpretation. We propose a formalism for an extremely close interaction of acoustic recognition and higher level analysis. Instead of a strict horizontal interface at the level of hypothesized word sequences or lattices, a vertical interface to the acoustic component is used that can be accessed from linguistic concepts of any degree of abstraction. As the linguistic knowledge is represented in the formalism of Semantic Networks and acoustic recognition is based on Hidden Markov Models the close interaction between the two components was termed Semantic Hidden Markov Networks.