The variance-covariance method is employed at low doses and in radiation fields of low dose rates from an241Am (4 nGy/s) and a90Sr (300 nGy/s) source. The preliminary applications and results illustrate some of the potential of the method, and show that the dose average of lineal energy or energy imparted can be determined over a wide range of doses and dose rates. The dose averages obtained with the variance-covariance method in time-varying fields, for which the conventional variance method is not suitable, agree well with results obtained under the condition of constant dose rate. The results are compared to data obtained in terms of the conventional single-event measurements. The method has evident advantages, such as facility and speed of measurement.