A double sequence $\mathbf{x}=\{x_{k,l}\}$ of points in a metric space $\mathbf{X}$ is slowly oscillating if for any given $\varepsilon>0$, there exist $\alpha (\varepsilon)>0$, $\delta=\delta (\varepsilon)>0$, and $N=N(\varepsilon)$ such that $d(x_{k,l},x_{s,t})<\varepsilon$ whenever $k,l\geq N(\varepsilon)$ and $k\leq s\leq (1+\alpha)k$, $l\leq t\leq(1+\delta)l$. We study continuity type properties of factorable double functions defined on a double subset $E\times E$ of $\mathbf{X}^2$ into $\mathbf{X}$, and obtain interesting results related to uniform continuity, sequential continuity, and a newly introduced type of continuity of factorable double functions defined on a double subset $E\times E$ of $\mathbf{X}^2$ into $\mathbf{X}$.