In the first part of the paper transformations mapping Toeplitz and Toeplitz-plus-Hankel matrices into generalized Cauchy matrices were studied. In this second part fast algorithms for LU-factorization and inversion of generalized Cauchy matrices are discussed. It is shown that the combination of transformation pivoting techniques leads to algorithms for indefinite Toeplitz and Toeplitz-plus-Hankel matrices that are more stable than the classical ones Special attention is paid to the symmetric and hermitian cases.