Abstract: The invention relates to a method of analyzing fluid influxes into an oil well from an underground formation. During a drilling mud transient flow state, the successive values of the rate Q.sub.i or pressure p.sub.r of injection of the drilling mud into the well and the successive values of the rate Q.sub.r or pressure p.sub.r of return of the drilling mud to the surface are measured. The changing values of the rate or pressure of injection are compared with the changing values of the return rate or pressure. From this comparison the nature and volume of the fluids that have penetrated into the well are determined.

Abstract: The invention relates to a method of real time control of fluid influxes into an oil well from an underground formation during drilling.The injection pressure p.sub.i and return pressure p.sub.r and the flow rate Q of the drilling mud circulating in the well are measured. From the pressure and flow rate values, the value of the mass of gas M.sub.g in the annulus is determined, and the changes in this value monitored in order to determine either a fresh gas entry into the annulus or a drilling mud loss into the formation being drilled.