A Doppler-free polarization spectrum of the D 1-SIGMA-u+ (upsilon',J')-X 1-SIGMA-g+ (upsilon",J") transition has been observed, and the molecular constants of the D 1-SIGMA-u+ state were determined. A remarkable variation of the vibrational spacing DELTA-G-upsilon with upsilon', and large deviations of DELTA-G-upsilon from the fitted DELTA-G-upsilon curve for upsilon' > 35 were analyzed. The potential curve of the perturbing state, which was identified as the bound (2)3-PI-u state, was estimated. By using an experimental setup where a collimated cesium beam is crossed at right angles by the laser beam, we measured the excitation spectra by monitoring separately the molecular fluorescence and the D2 or D1 atomic emission. We found that a predissociation of the D 1-SIGMA-u+ state occurred for upsilon' > 20, and the probability of predissociation increased with upsilon'. The measured upsilon' and J' dependence of the linewidth GAMMA showed a significant increase for upsilon' > 25. The predissociation of the D 1-SIGMA-u+ state is caused by a combination of spin-orbit interaction between the D 1-SIGMA-u+ (upsilon' J') and (2)3-PI-0u(e upsilon-J') levels, and the L-uncoupling interaction between the bound (2)3-PI-0u(e upsilon-J') and dissociative c 3-SIGMA-u+ (N = J'J') levels.