  The mass of a Cepheid is a fundamental parameter for studying the pulsation
and evolution of intermediate-mass stars. But determining this variable has
been a long-standing problem for decades. Detecting the companions (by
spectroscopy or imaging) is a difficult task because of the brightness of the
Cepheids and the close orbit of the components. So most of the Cepheid masses
are derived using stellar evolution or pulsation modeling, but they differ by
10-20%. Measurements of dynamical masses offer the unique opportunity to make
progress in resolving this mass discrepancy. The first problem in studying
binary Cepheids is the high contrast between the components for wavelengths
longer than 0.5 {\mu}m, which make them single-line spectroscopic binaries. In
addition, the close orbit of the companions (< 40 mas) prevents us from
spatially resolving the systems with a single-dish 8m-class telescope. A
technique able to reach high spatial resolution and high- dynamic range is
long-baseline interferometry. We have started a long-term program that aims at
detecting, monitoring and characterizing physical parameters of the Cepheid
companions. The GAIA parallaxes will enable us to combine interferometry with
single-line velocities to provide unique dynamical mass measurements of
Cepheids.
