We study the fixed membership problem for k-uniformly-limited and propagating ET0L systems (kulEPT0L systems). To this end, the algorithm given in [7] is applied. It follows that kulEPT0L languages are parsable in polynomial time. Since kulEPT0L languages are semi-linear [1] and kulEPT0L systems generate certain non-context-free languages, which capture the non-context-free phenomena occurring in natural languages, this is the last building block to show that kulEPT0L languages, for k ≥ 2, belong to the family of mildly context-sensitive languages.