Let the observation {y(k)} be generated by the multivariate ARMA process A(z)y(k) = C(z)w(k) with unknown coefficients theta(A), theta(C) and orders (p, r), where {w(k)} is a sequence of independent and identically distributed (i.i.d.) random vectors with zero mean and unknown covariance matrix R(w) > 0. A new method for estimating the orders (p, r) is introduced. In contrast to most of the existing results, the new method is not based on optimizing a certain criterion, and the order estimates given in the paper are rather easy to update computationally in comparison with the criterion-optimization-based methods when new data arrive. The method is then extended to determining the orders of ARMAX processes. Under reasonable conditions the estimates are proved to converge to the true orders with probability one as time tends to infinity.