We develop an a-posteriori error estimation for the finite element simulation of an advection-diffusion problem with anisotropic meshes. The error analysis is carried out by exploiting some recent interpolation error estimates for anisotropic meshes within the a-posteriori analysis framework proposed by Becker and Rannacher (1995, 1996, 1997) and Rannacher (1998). The target application is the transport of a solute (like oxygen or lipids) by the blood stream in a large artery