Diffusion of methyl yellow (MY) in the oligomeric host of n-alkanes and n-alcohols was studied by forced Rayleigh scattering as a function of the molecular weight and the viscosity of the medium. We observe that the diffusivity of the probe molecule follows a power law dependence on the molecular weight of the oligomers, D(MY)similar to M-alpha well. As the molecular weight of the oligomers increases, the exponent alpha shows a sharp transition from 1.88 to 0.91 near docosane (C22) in n-alkanes and from 1.31 to 0.60 near 1-hexadecanol (C16OH) in n-alcohols at 45 degrees C. A similar transition is also found in the molecular-dynamics simulation for the diffusion of a Lennard-Jones particle of a size similar to MY in n-alkanes. This transition deems to reflect a change of the dynamics of oligomeric chain molecules that the motion of the segments, not the entire molecules, becomes responsible for the transport of the probe molecule as the molecular weight of the oligomer increases. However, a weak but finite molecular weight dependence is observed above the transition point. Since it is well established that this molecular weight dependence disappears at high molecular weight medium, this indicates that the molecular weight of the oligomers is not high enough and the motion of the entire chain molecule is still correlated with the probe motion to some extent. The transition points in n-alkane and n-alcohol are in good agreement with the molecular weight at which the diffusional activation energy of MY reaches the asymptotic value, similar to 20 kJ/mol near n-docosane and similar to 30 kJ/mol near 1-hexadecanol.