Type I XRBs are thermonuclear flashes on the surface of neutron stars (NS) associated with mass-accretion from a companion star. Models of type I XRBs and their associated nucleosynthesis are physically complicated and extremely intense as regards the huge computational power required to model the physical processes played out, with the required precision to be truly representative. Until recently, because of these computational limitations, studies of XRB nucleosynthesis have been performed using limited nuclear reaction networks. In the bid to overcome this hurdle, parallel computing has been raised as the main permitting factor of yet more precise and computationally intensive simulations as it offers the potential to concentrate computational resources on intensive computational problems. In this Work, we present a parallelisation of two different applications; a one-zone (i.e. parameterized) nucleosynthesis code, and a one-dimensional (spherically symmetric), hydrodynamic code, in Lagrangian formulation (hereafter SHIVA code), built originally to model classical nova outbursts (José 1996; José & Hernanz 1998). The codes have been parallelised using the MPICH2 implementation of the Message Passing Interface (MPI) specification for the design of parallel applications using clusters of distributed workstations. As an example, to execute a hydrodynamic simulation along 200k time-steps, the SHIVA code requires (in its sequential, single-node version) about 147 hours (6.1 days) to complete when using a reduced nuclear network with 324 isotopes and 1392 nuclear reactions, and 688 hours (28.6 days) when using a network with 606 nuclides and 3551 nuclear reactions for the same number of time-steps. The post-processing nucleosynthesis code is a time-step loosely synchronous application with a very small problem size (limited by the number of isotopes of the nuclear network). As shown by the performance tests, this fact results in the worst possible scenario for parallelisation; results show that the performance of the parallel application is much worst than the sequential, 1-node version of the code. Our results show that it is therefore not possible to parallelise efficiently a post-processing nucleosynthesis code, and efforts in this regard should be avoided. On the contrary, the parallelised version of the SHIVA code yields excellent performance results. A speed-up factor of 26 is achieved in a simulation with a reduced network consisting of 324 isotopes and 1392 nuclear reactions when 42 processors are used in parallel to execute the application along 200k time-steps. On the other hand, an excellent speed-up factor of 35 is accomplished in a simulation with a reaction network up to 606 nuclides and 3551 nuclear reactions. Maximum speed-ups of ~41 and ~85 are predicted by the performance models when using 200 processors, for the reduced and extended simulations respectively. Our results will not only improve the quality of the simulations (and hence publications) in terms of better numerical approaches, finer approximations, and a considerably shorter time-to-publication, but also will allow taking advantage, if desired, of parallel supercomputing facilities like the Mare Nostrum at the Supercomputing Centre in Barcelona (BSC).