The paper first reviews the status of the Walsh-functions (WF) approach to the problem of parameter identification in continuous dynamical systems. The WF method of analysis and parameter estimation relies on the use of the so-called operational matrix for integration. For higher-order systems, the existing operational matrix has so far been applied after being raised to the required power. This procedure results in an accumulation of error at each stage of integration. To improve this situation, the paper introduces one-shot operational matrices for repeated integration (OSOMRI) via Walsh functions. The superiority of OSOMRI is demonstrated in problems of analysis and identification of higher-order systems. The paper then presents a direct noniterative method of parameter estimation for lumped linear systems in the presence of small unknown delays employing Walsh delay matrices developed recently by the authors. When the delay terms are not small, the results of this noniterative method will be considerably in error. However, these results can be taken as good initial values for the inevitable refining iterative shift algorithm of Prasada Rao and Sivakumar. The paper also presents an efficient multistep algorithm for parameter estimation in systems with large unknown time delays.