We present the parallel implementation on a transputer network of two preconditioned Lanczos-type schemes for the solution of unsymmetric sparse Linear systems: Bi-CGSTAB and TFQMR Solution of a number of sample tests shows that Bi-CGSTAB with ILU preconditioning is generally Faster than TFQMR, but do not achieve. a high degree of parallelize!ion. Better paraLlelization is obtained with the diagonal preconditioner, which uses less memory and allows therefore the solution of larger problems. With this preconditioner the TFQMR algorithm is found to be more robust than Bi-CGSTAB, but not always globally more efficient. The speed Ups obtained with 8 processors in this case reached a maximum of approximately 6.82, showing the high degree of parallelization achievable with the diagonal preconditioner. As in most massively parallel scenarios, however, the attainable speed ups are strongly dependent on the problem granularity.