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Time-dependent single molecule diffusion coefficients are discussed for a fluorescent probe molecule in lipid mixtures near a miscibility critical point. The calculations take advantage of the theoretical wave vector dependent composition diffusion coefficients obtained by Inaura and Fujitani [J. Phys. Soc. Jpn. 77, 114603 (2008)]. It is suggested that the diffusion of the probe molecule reflects in part the time-dependent composition diffusion near a critical point. The calculations show a striking biphasic time-dependent diffusion that switches from a faster diffusion at short times to a slower diffusion at a time approximately equal to πξ2/D where ξ is the correlation length and D is the composition diffusion coefficient at the switch time. This biphasic diffusion should be readily detectable experimentally.© 2012 American Institute of Physics.[http://dx. doi. org/10.1063/1.4768956]