Let \(X^ 0_ 1,...,X^ 0_ n\) be independent survival times of n individuals or items with common distribution \(F^ 0\) and corresponding density \(f^ 0\). Let \(U_ 1,...,U_ n\) be censoring random variables independent of the \(X^ 0_ i\)’s which are independent with common distribution H. Based on the observed pairs \((X_ i,\Delta_ i)\), \(i=1,...,n\), where \(X_ i=\min (X^ 0_ i,U_ i)\) and \(\Delta_ i=1\) if \(X^ 0_ i\leq U_ i\) and zero, otherwise, a kernel estimator of \(f^ 0\) in the form \[ f_ n(x)=h_ n^{-1}\sum^{n}_{j=1}s_ j K((x-Z_ j)/h_ n) \] is considered, where \(s_ j\) is the jump at \(Z_ j\) of the product-limit estimator of \(F^ 0\) and \(Z_ j\) denotes the j-th order statistic from \(X_ 1,...,X_ n\). Under a proportional hazards assumption, expressions for \(E[f_ n(x)]\) and \(var[f_ n(x)]\) are obtained and the limiting behavior is investigated.