We present the results of 6 years of spectroscopic monitoring of the Seyfert 1 galaxy Mrk 335. Each year, the observations span 5-7 months at a nominal sampling rate of one observation per week. Analysis of the spectroscopic observations shows clear coordinated variability in the continuum and in the broad H beta and He II lambda 4686 emission lines. The principal goal of this monitoring program is to measure the time delay between the continuum variations and the corresponding responses of the broad H beta and He II emission lines. We derive time delays of similar to 17 days for H beta and similar to 2 days for He II. From the spectral time series we construct average, root mean square, and difference spectra, which show that the broad H beta variations are confined to the core of the broad emission lines, whereas the He II variations take place across the full width of the profile. The He II emission line is about twice as broad as the H beta line. Comparison of the He II and H beta lags and line widths indicates that the BLR has a radially stratified ionization structure and that the highest velocity gas is closest to the continuum source. We also find no evidence for correlation between the line profile variations and the continuum and emission-line flux variations, as has been found in other cases. Rather, the line profile variations seem to imply dynamical changes in the BLR.