[en] Neutron scattering experiments with full polarization analysis have been performed with a single crystal of chromium to study the low-energy spin fluctuations in the transverse spin density wave (TSDW) state. A number of remarkable results have been found. Inelastic scattering observed close to the TSDW satellite positions at (1 ± δ,0,0) does not behave as expected for magnon scattering. In particular, the scattering corresponds to almost equally strong magnetization fluctuations both parallel and perpendicular to the ordered moments of the TSDW phase. As the Neel temperature is approached from below, scattering at the commensurate wavevector (1,0,0) increases in intensity as a result of critical scattering at silent satellites (1,0, ± δ) being included within the spectrometer resolution function. This effect, first observed by Sternlieb et al, does not account for all of the inelastic scattering around the (1,0,0) position, however, Rather, there are further collective excitations, apparently emanating from the TSDW satellites, which correspond to magnetic fluctuations parallel to the ordered TSDW moments. These branches have a group velocity that is close to that of (1,0,0) longitudinal acoustic (LA) phonons, but assigning their origin to magneto-elastic scattering raises other unanswered questions