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Let $\mathcal{I}_{d,g,r}$ be the union of irreducible components of theHilbert scheme whose general points represent smooth irreducible non-degeneratecurves of degree $d$ and genus $g$ in $\mathbb{P}^r$. Using a family of curvesfound on ruled surfaces over smooth curves of genus $\gamma$, we show that for$\gamma \geq 7$ and $g \geq 6 \gamma + 5$ the scheme $\mathcal{I}_{2g-4\gamma +1, g, g - 3\gamma + 1}$ acquires a non-reduced component $\mathcal{D}^{\prime}$such that $\dim T_{[X^{\prime}]} \mathcal{D}^{\prime} = \dim\mathcal{D}^{\prime} + 1$ for a general point $[X^{\prime}] \in\mathcal{D}^{\prime}$.

Components of the Hilbert Scheme of smooth projective curves using ruled surfaces II: existence of non-reduced components