This paper presents a detailed case study of small-signal stability analysis for the Cigré DC-grid test system. The presented investigations are intended for identifying critical modes of interaction between different parts of the electrical system and the controllers in multi-terminal HVDC (MTDC) schemes. Oscillatory and critical modes of the system are investigated by modal analysis, including participation factor analysis and studies of the parameters sensitivity. The potentially unstable modes are investigated by calculating the participation factors of the system, which identify the influencing components. The sensitivity of the eigenvalues to the control parameters is also presented in order to reach an improved control design for MTDC with sufficient damping and enhanced dynamic response. Time-domain simulation results are further presented in order to verify the transient performance of the control system.