connecting ac and dc sources together in series
You should've provided us with more details. For instance, knowing what components you're using for DC and AC sources could lead to a specific answer.

In general, his behavior may be caused by either of the following:


The current through your circuit exceeding the limit of one of the sources (usually AC), in which case strange behavior can be seen (the exact behavior depends on the components).
Your AC source is "grounded" - one of its outputs (usually the "-") must be connected to the ground of the circuit (I'm assuming here that the ground of your circuit is defined by the "-" output of the DC source).


Since I believe that your issue is #2 above (and because it is trivial to check for #1), you have few options (the ones I can think of):


The answer by @Jim Dearden is the most robust way to proceed with (maybe not the exact configuration, but the employment of op-amp)
However, there might be shorter solution: check your DC power supply spec. If its outputs may be floating, then you can switch places between AC and DC supplies in you circuit. This will allow you to satisfy "grounded" constraint of your AC supply, while keeping both supplies in series.