  Looptrees have recently arisen in the study of critical percolation on the
uniform infinite planar triangulation. Here we consider random infinite
looptrees defined as the local limit of the looptree associated with a critical
Galton--Watson tree conditioned to be large. We study simple random walk on
these infinite looptrees by means of providing estimates on volume and
resistance growth. We prove that if the offspring distribution of the
Galton--Watson process is in the domain of attraction of a stable distribution
with index $\alpha\in(1,2]$ then the spectral dimension of the looptree is
$2\alpha/(\alpha+1)$.
