In this thesis a new method for the analysis of power transients in a nuclear reactor is developed, which is more accurate than the present state-of-the-art methods. Transient analysis is important tool when designing nuclear reactors, since they predict the behaviour of a reactor during changing conditions, such as a control-rod movement, induced by an operator, or an accident scenario. The current methods for transient analysis apply deterministic solvers to calculate the neutronic response, but not only do these deterministic solvers always need to discretise the problem, they also often apply more fundamental approximations such as homogenization or diffusion. Therefore a stochastic method is needed, which only has a statistical uncertainty. A challenge for applying the Monte Carlo method on transient analysis, is the different types of particles which must be simulated in a single simulation. It is common for a neutronics calculation to simulate the prompt neutrons, however the simulation of precursors is new. The main challenge when simulating precursors lies in their long lifetime, which is seconds, whereas the prompt neutrons have a lifetime of microseconds. This has been solved by dividing the transient problem into time intervals and forcing the precursors to produce a delayed neutron is all time intervals. This will ensure prompt-neutron chains in all intervals. The prompt neutrons will form prompt-neutron chains, which poses another challenge for the Monte Carlo method. The chain length of these prompt neutrons varies a lot and the can also split into many branches, which averages out in a real power reactor, but is difficult to simulate on a computer. To improve the chain-length statistics, a new variance reduction technique is developed, which dictates that a single neutron will emerge from each interaction. This emerging neutron can be the result of a scattering event or a fission event. Finally, a dynamic simulation scheme, which can run in parallel, has been devised, simulating all time intervals consecutively. Also, a method for sampling the initial conditions is created and this scheme is implemented in a purpose-built Monte Carlo code and in a general-purpose Monte Carlo code. The two codes have been tested in several cases and they behave as expected, agreeing with deterministic method where expected, but deviating when the deterministic methods are no longer valid. In order to simulate realistic transients in a power reactor, feedback has to be taken into account. To achieve this, the dynamic Monte Carlo method has been coupled to a thermal-hydraulics code, using an explicit scheme. The results of this coupled simulation are compared to a state-of-the-art coupled diffusion calculation in a NURISP-benchmark calculation and the results agree well, except for a small deviation towards the end. The exact source of this deviation should be further investigated, but the difference is small, when realising that there is already a deviation in the steady-state results. The results demonstrate the feasibility of performing a fully dynamic transient analysis, using only Monte Carlo for the neutronics part of the calculation. Transients can now be calculated, with detailed modelling of any complex geometry and with continuous energy, which is especially useful for newly developed reactor types and one-of-a-kind research reactors.