This thesis presents a case study about the condition monitoring of the twin-screw multiphase pump in the subsea field to demonstrate how condition monitoring techniques can be applied for subsea equipment. Firstly a FMECA (Failure modes, effects, and criticality analysis) worksheet is carried out to identify the critical components of a twin-screw multiphase pump. Among the identified critical components, the mechanical seal and the twin screws are determined as study objects. For the condition monitoring of the mechanical seal, four different methods are introduced to detect the conditions of the mechanical seal. Then a physics-based model and a data-driven model are presented respectively as the diagnosis and prognosis models for the case of mechanical seals. For the twin screws, by learning the wear mechanism of the screws, the pressure distribution along the screw axis is decided to be measured to analyse the wear conditions of the twin screws. Afterwards Hidden Markov Model (HMM) is proposed for the failure diagnosis and prognosis. In addition a numerical example is computed to prove that HMM has the ability to identify the current wear state and predict the remaining useful life of the twin screws.