The recently introduced Oxford Nanopore MinION platform generates DNA sequence data in real-time. This has great potential to shorten the sample-to-results time and is likely to have benefits such as rapid diagnosis of bacterial infection and identification of drug resistance. However, there are few tools available for streaming analysis of real-time sequencing data. Here, we present a framework for streaming analysis of MinION real-time sequence data, together with probabilistic streaming algorithms for species typing, strain typing and antibiotic resistance profile identification. Using four culture isolate samples, as well as a mixed-species sample, we demonstrate that bacterial species and strain information can be obtained within 30 min of sequencing and using about 500 reads, initial drug-resistance profiles within two hours, and complete resistance profiles within 10 h. While strain identification with multi-locus sequence typing required more than 15x coverage to generate confident assignments, our novel gene-presence typing could detect the presence of a known strain with 0.5x coverage. We also show that our pipeline can process over 100 times more data than the current throughput of the MinION on a desktop computer.