Let be an matrix with independent standard complex Brownian entries and set . This is a process version of the Laguerre ensemble and as such we shall refer to it as the Laguerre process;. The purpose of this note is to remark that, assuming , the eigenvalues of evolve like independent squared Bessel processes of dimension , conditioned (in the sense of Doob) never to collide. More precisely, the function is harmonic with respect to independent squared Bessel processes of dimension , and the eigenvalue process has the same law as the corresponding Doob -transform. In the case where the entries of are real Brownian motions, is the Wishart process considered by Bru (1991). There it is shown that the eigenvalues of evolve according to a certain diffusion process, the generator of which is given explicitly. An interpretation in terms of non-colliding processes does not seem to be possible in this case. We also identify a class of processes (including Brownian motion, squared Bessel processes and generalised Ornstein-Uhlenbeck processes) which are all amenable to the same -transform, and compute the corresponding transition densities and upper tail asymptotics for the first collision time.