Programmable diffractive optical elements (DOEs) with axial response have many interesting applications, including diffractive lenses, axicons, and optical tweezers. In all these cases, it is essential to properly select the modulation configuration of the spatial light modulator (SLM) where the DOE is displayed, in order to avoid the undiffracted zero order component that appears on axis and overlaps the desired axial response. However, in general, the chromatic dispersion in liquid crystal SLMs prevents the cancellation of the zero order for a broadband light source, thus limiting the possibilities for polychromatic programmable axial DOEs. We operate a ferroelectric liquid crystal on silicon display with polychromatic illumination and with a specific polarization configuration that provides binary -phase modulation for all wavelengths. Since this type of modulation cancels the undiffracted zero order, we use this SLM to display DOEs with axial response. Moreover, chromatic control is achieved by time-multiplexing sequences of properly scaled DOEs with the corresponding selection of the input wavelength by means of an electronically controlled color-filter wheel. The presented experimental results include wavelength-controlled diffraction gratings, axicons, and vortex-producing lenses.