Following recent work on $N=1\mathrm{}$ rigid supersymmetry in the curved space $S^3$, models with extended supersymmetry are examined. Unusual superalgebras with $N=2\mathrm{}$ and $N=3\mathrm{}$ appear. These reduce to appropriate superalgebras in Minkowski space if the curvature is taken to zero. It is shown that possible anomalies in some of the bosonic currents cancel between the various spin-½ fermions present in these theories. Extended supersymmetry is therefore anomaly-free in $R\times S^3$.

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