Is it possible to model a min-max-problem using pyomo
I think yes, but unless you find a clever way to reformulate your model, it might not be very efficent. 
You could solve all possiblity of max(g_m(x)), then select the solution with the lowest objective function value. 
I fear that the max operation is not something you can add to a minimization model, since it is not a mathematical operation, but a solver operation. This operation is on the problems level. Keep in mind that when solving a model, Pyomo requires as argument only one sense of optimization (min or max), thus making it unable to understand min-max sense. Even if it did, how could it knows what to maximize or minimize? This is why I suggest you to break your problem in two, unless you work on its formulation.
Ist it possible to formulate a min-max-optimization problem of the following form in pyomo:
min(max(g_m(x)) s.t. L
where g_m are nonlinear functions (actually constrains of another model) and L is a set of linear constrains?
How would I create the expression for the objective function of the model?
The problem is that using max() on a list of constraint-objects returns only the constraint possessesing the maximum value at a given point.