Using kernel estimates of the Parzen type, a naive sequential nonparametric density estimation procedure is developed. The asymptotic distribution structure of the stopping variable is examined. The stopping variable is shown to have finite moments of ail order and is shown to be dosed. The stopping variableNdepends on some preassigned error\varepsilon, and it is shown thatNdiverges strongly to\inftyas\varepsilonconverges to zero. Finally, with\hat{f}_n(x)being a kernel-type estimator, it is shown that\hat{f}_N(X)converges tof(x), the true density atx, with probability one as\varepsilonconverges to zero.