Summary As a classical control model, the skyhook damper configuration can be used to adapt to changes in road conditions rather than that in load conditions. Conversely, as a newly developed control model, the skyhook inerter configuration can be used to adapt to variation of load conditions but not that of road conditions. In order to solve or at least reduce the conflict between load and road adaptability, a double‐skyhook configuration that combines a skyhook inerter and a skyhook damper is proposed in this paper to adapt to changes in both road and load conditions. Two semi‐active means to realize the double‐skyhook configuration are investigated separately; one is using two mutually independent devices (a semi‐active inerter and a semi‐active damper); the other is using a semi‐active device combining an adjustable inerter and an adjustable damper. Three control strategies—the independent double‐skyhook control, the inertance‐based double‐skyhook control, and the damping‐based double‐skyhook control—are proposed for the devices to approximate the skyhook inerter and damper. To simulate the skyhook inertance and damping forces realistically, a model of the combined semi‐active device is established and verified by a prototype test. Numerical simulations based on such a model are performed to demonstrate the effectiveness of these strategies and to achieve the desired load and road adaptabilities. As a consequence, the semi‐active suspensions with the double‐skyhook controls can offer a much smoother and more constant ride quality than the suspensions with the single‐skyhook (skyhook inertance and skyhook damping) controls and the passive suspension, which effectively demonstrates the necessity and benefit of introducing the double‐skyhook control to vehicle suspension.