The dynamical spin structure factor and the Raman response are calculated for structurallydimerized and spin-Peierls chains in a magnetic field, using exact diagonalization techniques. Inboth cases there is a spin liquid phase composed of interacting singlet dimers at small fields h<hc1,an incommensurate regime (hc1<h<hc2) in which the modulation of the triplet excitation spectraadapts to the applied field, and a fully spin polarized phase above an upper critical field hc2. Forstructurally dimerized chains, the spin gap closes in the incommensurate phase, whereas spin-Peierlschains remain gapped. In the spin liquid regimes, the dominant feature of the triplet spectra is aone-magnon bound state, separated from a continuum of states at higher energies. There are alsoindications of a singlet bound state above the one-magnon triplet.