In this paper we discuss the problem of estimating conjugate times along smooth singular or bang-bang extremals. For smooth extremals conjugate times can be defined in the generic case by using the intrinsic second order derivative or the exponential mapping. An algorithm is given which was implemented in the SR-case to compute the caustic or in recent applied problems. We investigate briefly the problem of using this algorithm in the bang-bang case by smoothing the corners of extremals.