This paper deals with the phenomena of slowly varying oscillations of moored vessels and presents procedures for predicting their values in wind and waves. 2nd-order forces (drifting forces) in regular waves were clearly induced by kinetic energy flow rate of progressive waves which were determined by linear velocity potentials. The mean values of 2nd-order wave forces, presented in this paper, are the same results of Maruo's formula in regular waves and irregular waves, and the slowly varying ones are the same results of the formula derived by Newman and Faltinsen and Løken. Simple formula, based on the steady-state displacement, for predicting slowly varying oscillations due to 2nd-order wave exciting forces is presented in this paper (formula (41)). Numerical results are in fairly good agreement with Pinkster's calculations, and the test results and the computer simulations conducted by Remery and Hermans as shown in Fig. 7. Consequently, the formula presented herein will be usefull for the practical mooring design.