In an increasingly globalized world, situations in which people of different native tongues have to communicate with each other become more and more frequent. In many such situations, human interpreters are prohibitively expensive or simply not available. Automatic spoken language translation (SLT), as a cost-effective solution to this dilemma, has received increased attention in recent years. For a broad number of applications, including live SLT of lectures and oral presentations, these automatic systems should ideally operate in real time and with low latency. Large and highly specialized vocabularies as well as strong variations in speaking style – ranging from read speech to free presentations suffering from spontaneous events – make simultaneous SLT of lectures a challenging task. This paper presents our progress in building a simultaneous German-English lecture translation system. We emphasize some of the challenges which are particular to this language pair and propose solutions to tackle some of the problems encountered.