Load-dependent closed queueing networks are difficult toapproximate since their analysis requires to consider state-dependent service demands. Commonly employed evaluationtechniques, such as mean-value analysis, are not equallyefficient in the load-dependent setting, where mean queue-lengths are insufficient alone to recursively determine themodel equilibrium performance.In this paper, we contribute to addressing this problem byobtaining novel solutions for the normalizing constant of stateprobabilities in the load-dependent setting. For single-classload-dependent models, we provide the first explicit exactformula for the normalizing constant that applies to modelswith arbitrary load-dependent rates, while retainingO(1)complexity with respect to the total population size. Fromthis result, we derive two novel integral forms for the normal-izing constant in multiclass load-dependent models, whichinvolve integration in the real and complex domains. Thepaper also illustrates through experiments the computationalgains and accuracy of the obtained expressions.