Let $T$ be a complete countable first order theory and $\lambda$ an uncountable cardinal. Theorem 1. If $T$ is not superstable, $T$ has $2^\lambda$ resplendent models of power $\lambda$. Theorem 2. If $T$ is strictly superstable, then $T$ has at least $\min(2^\lambda,\beth_2)$ resplendent models of power $\lambda$. Theorem 3. If $T$ is not superstable or is small and strictly superstable, then every resplendent homogeneous model of $T$ is saturated. Theorem 4 (with Knight). For each $\mu \in \omega \cup \{\omega, 2^\omega\}$ there is a recursive theory in a finite language which has $\mu$ resplendent models of power $\kappa$ for every infinite $\kappa$.