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We develop a new algorithm for the quantisation of systems with first-classconstraints. Our approach lies within the (History Projection Operator)continuous-time histories quantisation programme. In particular, theHamiltonian treatment (either classical or quantum) of parameterised systems ischaracterised by the loss of the notion of time in the space of true degrees offreedom (i.e. the `problem of time'). The novel temporal structure of the HPOtheory (two laws of time transformation that distinguish between the temporallogical structure and the dynamics) persists after the imposition of theconstraints, hence the problem of time does not arise. We expound the algorithmfor both the classical and quantum cases and apply it to simple models.Comment: 34 pages, Late

Histories quantization of parameterized systems: I. Development of a general algorithm