pontocerebellar fibers pontocerebellar fibers the pontocerebellar fibers are the second order neuron fibers of the corticopontocerebellar tracts that cross to the other side of the pons and run within the middle cerebellar peduncles, from the pons to the contralateral cerebellum. pontocerebellar fibersscheme showing the connections of the several parts of the brain.detailsidentifierslatinfibrae pontocerebellaresneuronames1345ta98a14.1.05.110ta25849fma75215anatomical terms of neuroanatomy the term "corticopontocerebellar" is the entire pathway from the cerebral cortex to the contralateral cerebellum.