Abstract  Subject of the paper are centro-symmetric and centro-skewsymmetric Toeplitz-plus-Hankel matrices with the property that all central submatrices are nonsingular. Fast algorithms are presented that solve an n×n system of equations with O(n ²) operations in sequential and O(n) operations in parallel processing and compute the ZW-factorization with the same computational complexity. These algorithms are more efficient than existing algorithms because they fully exploit the symmetry properties of the matrices.