病気のため控訴期限を過ぎてしまった場合、オランダの裁判所判決に対して控訴できますか？

It depends on what you mean by an “appeal.” If the judgment was a verstekvonnis, there are in principle still possibilities to challenge it (zuiveren). In that situation, you may be able to file an opposition (verzet). While this is formally an appeal, it functions in practice as a reopening of the proceedings, allowing the case to be heard again on the merits. If, however, the judgment was rendered after regular proceedings, meaning that your arguments were filed and the court heard both sides, the situation is much more difficult. Although exceptional circumstances can be imagined, acceptance of a late appeal in such cases is extremely rare.

In any context, it is crucial to examine how the judgment was served, i.e. whether and when it was formally delivered to you in such a way that you became aware of the decision. In addition, in all cases it is relevant whether you performed any “act of awareness” (daad van bekendheid), such as sending an email or otherwise acting in a way that demonstrates that you had knowledge of the judgment.