The left, right and doubly truncated 3-parameter lognormal density functions are given and their moments evaluated. Moment estimation of the three parameters ,  and  is discussed and maximum likelihood equations obtained in all cases. Solutions of the ML equations are computed using the methods proposed by [2] and [3]. The elements of the information matrices are determined and the variances of estimates computed. Approximate biases in the estimates  ,  and  are derived and computed in all cases of left, right and double truncation.  and are shown to be approximately unbased.  is shown to be biased and its approximate bias is given. The bias in  is shown to tend to zero for large sample size.