We propose P systems in which the solutions of previously executed computations can be stored in sub-systems composed by a number of membranes which act as memory elements. When a new input is inserted into the system, the computation on that input is started in parallel with the search for the corresponding solution in all memory membranes. If the solution is found in memory, then a copy of it is expelled from that memory membrane; the search in all other memory membranes is stopped, and the same is done with the computing sub-system. If no solution for that input is found, then the computation produces the solution, which is subsequently stored in a memory cell.