Max-mixture processes are defined as Z = max(aX, (1 − a)Y) with X an asymptotic dependent (AD) process, Y an asymptotic independent (AI) process and a ∈ [0, 1]. So that, the mixing coefficient a may reveal the strength of the AD part present in the max-mixture process. In this paper we focus on two tests based on censored pairwise likelihood estimates. We compare their performance through an extensive simulation study. Monte Carlo simulation plays a fundamental tool for asymptotic variance calculations. We apply our tests to daily precipitations from the East of Australia. Drawbacks and possible developments are discussed.