1. A Welding method for implementing and monitoring a welding process with a welding rod which melts in an arc which is supplied with power from at least one automatically controlled power source, whereby the power source and a feeding device for the welding rod are controlled by means of a control device, and whereby at least one control variable such as welding current, welding voltage or resistance is measured or calculated from characteristic variables of the arc during the welding process, and different welding parameters or values for the control variable are stored in a memory during the welding process, wherein a first and a second time interval with different durations and a scanning rate are set in order to determine values of the characteristic variable, and the values of the characteristic variable are stored with every scan, after which, at an instant, a first mean value and a second mean value are calculated by the control device as the control variable from stored values of the characteristic variable which lie in at least one of the first or second time intervals lying earlier in time than said instant, and then an upper threshold value and a lower threshold value are calculated from the first mean value of the first time interval and the control variable is compared with said upper threshold value and with said lower threshold value.