We evaluated the transport of polymeric particles internalized into living cancer cells. The mean-square displacement demonstrates superdiffusion with a scaling exponent of 1.25. Scaling exponents of a range of displacement moments are bilinear with moment order, exhibiting slopes of 0.6 and 0.8. Thus, we present experimental evidence of strong anomalous diffusion. Bilinearity indicates that particle motion is composed of subdiffusive regimes separated by active yet nonballistic flights. We discuss the results in terms of particle interactions with their microenvironment.