We demonstrate a three step laser stabilisation scheme for excitation to nP and nF Rydberg states in 85Rb, with all three lasers stabilised using active feedback to independent Rb vapour cells. The setup allows stabilisation to the Rydberg states 36P3/2 to 70P3/2 and 33F7/2 to 90F7/2, with the only limiting factor being the available third step laser power. We study the scheme by monitoring the three laser frequencies simultaneously against a self-referenced optical frequency comb. The third step laser, locked to the Rydberg transition, displays an Allan deviation of 30 kHz over 1 second and < 80 kHz over 1 hour. The scheme is very robust and affordable, and it would be ideal for carrying out a range of quantum information experiments.
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