Summary: The purpose of the current paper is to combine the classical results of Kaplan (1970) and Ehrhardt (1984) for stochastic leadtime problems with recent work of Morton and Pentico (1991), which assumed zero lag, to obtain near-myopic bounds and heuristics for the nonstationary stochastic leadtime problem with arbitrary sequences of demand distributions, and to obtain planning horizon results. Four heuristics have been tested on a number of different demand scenarios over a number of random trials for four different leadtime distributions. The myopic (simplest) heuristic performs well only for moderately varying problems without heavy end of season salvaging, giving errors for this type of problem that are less than 1.5%. However, the average error for the myopic heuristic over all scenarios tested is 20.0%. The most accurate heuristic is the near-myopic heuristic which averages 0.5% from optimal across all leadtime distributions with a maximum error of 4.7%. The average error increases with increase in variance of the leadtime distribution.