We formulate a risk-averse two-stage stochastic linear programming problem in which unresolved uncertainty remains after the second stage. The objective function is formulated as a composition of conditional risk measures. We analyze properties of the problem and derive necessary and sufficient optimality conditions. Next, we construct two decomposition methods for solving the problem. The first method is based on the generic cutting plane approach, while the second method exploits the composite structure of the objective function. We illustrate their performance on a portfolio optimization problem.