  Unstable pressure and u-equilibrium states are introduced and investigated
for a partially hyperbolic diffeomorphsim $f$. We define the u-pressure $P^u(f,
\varphi)$ of $f$ at a continuous function $\varphi$ via the dynamics of $f$ on
local unstable leaves. A variational principle for unstable pressure $P^u(f,
\varphi)$, which states that $P^u(f, \varphi)$ is the supremum of the sum of
the unstable entropy and the integral of $\varphi$ taken over all invariant
measures, is obtained. U-equilibrium states at which the supremum in the
variational principle attains and their relation to Gibbs u-states are studied.
Differentiability properties of unstable pressure, such as tangent functionals,
Gateaux differentiability and Fr\'{e}chet differentiability and their relations
to u-equilibrium states, are also considered.
