Truncation or censoring of the response variable in a regression model is a problem in many applications, e.g. when the response is insurance claims or the durations of unemployment spells. We introduce a local polynomial regression estimator which can deal with such truncated or censored responses. For this purpose, we use local versions of the STLS and SCLS estimators of Powell (1986) and the QME estimator of Lee (1993) and Laitila (2001). The asymptotic properties of our estimators, and the conditions under which they are valid, are given. In addition, a simulation study is presented to investigate the finite sample properties of our proposals.