With the aim of significantly increasing the modeling capability of Petri nets, we suggest that models involve parameters to represent the weights of arcs, or the number of tokens in places. We consider the property of coverability of markings. Two general questions arise: " Is there a parameter value for which the property is satisfied? " and " Does the property hold for all possible values of the parameters? ". We show that these issues are undecidable in the general case. Therefore, we also define subclasses of parameterised networks, depending on whether the parameters are used on places, input or output arcs of transitions. For some subclasses, we prove that certain problems become decidable, making these subclasses more usable in practice.