Nonlinear model predictive control (NMPC) has been popular in many applications, especially when constraint satisfaction is critical. However, due to plant-model mismatch and disturbances, robust NMPC generally faces three challenges: robust performance, real-time implementation, and stability. In this paper, we propose a parallelizable advanced-step multistage NMPC (as-msNMPC), which provides a non-conservative robust control solution that explicitly addresses two types of uncertainty: model parameters and unmeasured noise. The first type is attended to by incorporating scenario trees and the second by applying nonlinear programming (NLP) sensitivity. In addition, robust stability concepts have been discussed for both ideal multistage NMPC (ideal-msNMPC) and as-msNMPC. Under suitable assumptions, as-msNMPC has demonstrated input-to-state practical stability properties with the presence of two types of uncertainty. Lastly, the as-msNMPC framework has been applied to continuous stirred tank reactor (CSTR) and quad-tank case studies for tracking setpoints to demonstrate its performance in robustness and efficiency. (C) 2019 Elsevier Ltd. All rights reserved.