Consider the affine stochastic delay differential equation (SDDE)
dX(t) = \int_{-r}^0 X(t+s)a(ds)dt + dW(t) (1)
where a(.) is an arbitrary finite signed measure on [-r,0] and W(.) is a standard Wiener process. Assume a(.) belongs to some family (a_{ heta}, heta\in\Theta) with \Theta\subset R^k. The maximum-likelihood-estimator \hat{ heta}_T based on continuous observation of (X(t), t \leq T) is constructed and its asymptotic behaviour is determined. The great variety of possible limit behaviour is surprising.