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We present the largest near-infrared (NIR) data sets, $JHKs$, ever collectedfor classical Cepheids in the Magellanic Clouds (MCs). We selected fundamental(FU) and first overtone (FO) pulsators, and found 4150 (2571 FU, 1579 FO)Cepheids for Small Magellanic Cloud (SMC) and 3042 (1840 FU, 1202 FO) for LargeMagellanic Cloud (LMC). Current sample is 2--3 times larger than any sampleused in previous investigations with NIR photometry. We also discuss optical$VI$ photometry from OGLE-III. NIR and optical--NIR Period-Wesenheit (PW)relations are linear over the entire period range ($0.0<\log P_{\rm FU} \le1.65$) and their slopes are, within the intrinsic dispersions, common between theMCs. These are consistent with recent results from pulsation models andobservations suggesting that the PW relations are minimally affected by themetal content. The new FU and FO PW relations were calibrated using a sample ofGalactic Cepheids with distances based on trigonometric parallaxes and Cepheidpulsation models. By using FU Cepheids we found a true distance moduli of$18.45\pm0.02{\rm(random)}\pm0.10{\rm(systematic)}$ mag (LMC) and$18.93\pm0.02{\rm(random)}\pm0.10{\rm(systematic)}$ mag (SMC). These estimatesare the weighted mean over ten PW relations and the systematic errors accountfor uncertainties in the zero-point and in the reddening law. We found similardistances using FO Cepheids($18.60\pm0.03{\rm(random)}\pm0.10{\rm(systematic)}$ mag [LMC] and$19.12\pm0.03{\rm(random)}\pm0.10{\rm(systematic)}$ mag [SMC]). These new MCdistances lead to the relative distance, $\Delta\mu=0.48\pm0.03$ mag (FU, $\logP=1$) and $\Delta\mu=0.52\pm0.03$ mag (FO, $\log P=0.5$),which agrees quitewell with previous estimates based on robust distance indicators.

On the distance of the Magellanic Clouds using Cepheid NIR and optical-NIR Period Wesenheit Relations