The paper provides a kind of Klimko-Nelson theorems alternative in the case of conditional least-squares and Mestimators for array time series, when the assumptions of almost sure convergence cannot be established. We do not assume stationarity nor even local stationarity. In addition, we provide sufficient conditions for two of the assumptions and two theorems for the evaluation of the information matrix in array time series. In addition to timedependent models, illustrations to a threshold model and to a count data model are given.