We define a symbolic determinisation procedure for a class of infinite-state systems, which consists of automata extended with symbolic variables that may be infinite-state. The subclass of extended automata for which the procedure terminates is characterised as bounded lookahead extended automata. It corresponds to automata for which, in any location, the observation of a bounded-length trace is enough to infer the first transition actually taken. We discuss applications of the algorithm to the verification, testing, and diagnosis of infinite-state systems