with no (fixed) upper limit on working hours.

In other words, you get a monthly salary and you carry out your duties...

http://www.djoef.dk/r-aa-dgivning/ans-ae-ttelsesvilk-aa-r/fu...

Du er ansat uden højeste tjenestetid. Det betyder, at du i et vist omfang er forpligtet til at udføre arbejde udover 37 timer om ugen. I hvilket omfang du får betaling for det, fremgår af merarbejdsreglerne.

http://www.lederne.dk/KommendeLedere/Din ansaettelse/kontrak...

Hvad siger lovgivningen om arbejdstid?
Arbejdstiden er ikke lovmæssigt reguleret på det private område, men fastlægges i kollektive overenskomster eller individuelle kontrakter.

Et EU-direktiv fastsætter, hvordan arbejdstiden må tilrettelægges, herunder det forhold, at der ikke, i forhold til den enkelte arbejdsgiver, må arbejdes mere end gennemsnitlig 48 timer om ugen tilrettelagt over en periode på fire måneder.

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Danish employment law is based on collective agreements and individual contracts, which are often more or less modelled on the Salaried Workers' Act (Funktionærloven)
or occasionally Tjenestemandsloven (Statute relating to Civil Servants).

Collective agreements will typically have rules about working hours and overtime, with overtime pay, but this contract will go on to stipulate that there is no overtime pay as such, or under which conditions extra payments will be made.

It also yused to mean quite horrendous working hours in some cases, until the EU Directive was introduced, capping the working week at 48.

60 hours a week, for several weeks in a row, were not unknown, despite the efforts of DJØF and others.