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We combine near-infrared photometry obtained with the VLT/ISAAC instrument and archival HST/WFPC2 optical images to determine VIK magnitudes and colours of globular clusters in two early-type galaxies, NGC 3115 and NGC 4365. The combination of near-IR and optical photometry provides a way to lift the age-metallicity degeneracy. For NGC 3115, the globular cluster colours reveal two major sub-populations, consistent with previous studies. By comparing the V-I, V-K colours of the NGC 3115 globular clusters with stellar populations models, we find that the colour difference between the two >10Gyr old major sub-populations is primarily due to a difference in metallicity. We find Δ[Fe/H]=1.0±0.3dex and the blue (metal-poor) and red (metal-rich) globular cluster sub-populations being coeval within 3Gyr. In contrast to the NGC 3115 globular clusters, the globular cluster system in NGC 4365 exhibits a more complex age and metallicity structure. We find a significant population of intermediate-age very metal-rich globular clusters along with an old population of both metal-rich and metal-poor clusters. Specifically, we observe a large population of globular clusters with red V-K colours but intermediate V-I colours, for which all current stellar population models give ages and metallicities in the range ∼2-8Gyr and ∼0.5Z_☉-3Z_☉, respectively. After 10Gyr of passive evolution, the intermediate-age globular clusters in NGC 4365 will have colours which are consistent with the very metal-rich population of globular clusters in giant elliptical galaxies, such as M 87. Our results for both globular cluster systems are consistent with previous age and metallicity studies of the diffuse galactic light. In addition to the major globular cluster populations in NGC 3115 and NGC 4365 we report on the detection of objects with extremely red colours (V-K>3.8mag), whose nature could not ultimately be revealed with the present data.