Where do harmonics come from?
It appears that your understanding of harmonics is not entirely correct yet. Your example of two sinusoids with frequencies $f_1$ and $f_2$ can actually be explained in terms of harmonics IF
$$f_1=n_1f_0\quad\text{and}\quad f_2=n_2f_0,\qquad n_1,n_2\in\mathbb{Z^+}\tag{1}$$
is satisfied for some positive $f_0$. Note that this means that the ratio $f_1/f_2$ is rational. In that case the resulting sum is periodic. Choosing the smallest possible integer values of $n_1$ and $n_2$ such that $(1)$ is satisfied will allow you to compute the fundamental frequency $f_0$ of the resulting waveform.
In the case of your example we have $f_1=100$ and $f_2=201$ (units don't matter here). So we get $n_1=100$, $n_2=201$, and $f_0=1$ (same units as $f_1$ and $f_2$). So the sum is periodic with fundamental frequency $f_0=1$, even though the Fourier series coefficient of the fundamental is zero! Hence, we have a periodic signal with two harmonics and no fundamental. Nevertheless, the (fundamental) frequency of that signal equals $f_0=1$ (check that!).
With the period $T=1/f_0=1$ we have
$$x(t+T)=\sin\big[2\pi\cdot 100(t+T)\big]+\sin\big[2\pi\cdot 201(t+T)\big]=x(t)\tag{2}$$
where the last equality follows from the fact that we add an integer multiple of $2\pi$ to the argument of $\sin(x)$, which of course has period $2\pi$. Note that this doesn't show that $T$ is the smallest possible period, i.e., that $f_0$ is the largest possible fundamental frequency, but I trust that you can easily verify that.