In the noiseless case, the identification of a grey-box model can be posed as a feasibility problem, i.e. determining if existent - and if so - finding a parameter vector such that the parametric model equals the actual model (or its associated input-output data). Being that in this thesis we are interested in continuous-time grey-box identification, we shall be dealing with models that allow for forming a direct relationship with physical meaningful quantities. Such models include the state space representation and the matrix differential equation. In general, identifying such grey-box models turns out to be a non-convex problem. In this thesis, we initially review a framework which allows us to solve feasibility problems which have bilinear constraints. It turns out that most of the aforementioned non-convexities can be captured into a single bilinear matrix equation. However, the resulting feasibility problem, including the bilinear matrix equations, makes the overall search for the actual parameter vector NP-hard. In order to come up with numerical tractable algorithms, we use a heuristic known as Sequential Convex Relaxation to relax the bilinear equality constraints. This iterative scheme is flexible enough to allow for additional (in)equality constraints, possibly resembling any other physical constraints. We explore two different approaches to identify both the state space model and the matrix differential equation; one, by directly identifying the model from the given frequency response function; two, by first identifying a black-box model before performing a small scale optimization problem, transforming the black-box model such that it fits the grey-box parameterization. In addition, we present a novel method which uses the Power Spectral Density to estimate a 2nd order model. All methods are numerically validated.