We construct time and radial dependent solutions that describe p-branes in chargeless S-brane backgrounds. In particular, there are some new M5-and D3-branes among our solutions which have AdS limits and contain a cosmological singularity as well. We also find a time-dependent version of the dyonic membrane configuration in 11-dimensions by applying a Lunin-Maldacena deformation to our new M5-brane solution.