We consider reduced quantum electrodynamics (  <math> <msub> <mtext>RQED</mtext> <mrow> <msub> <mi>d</mi> <mi>γ</mi> </msub> <mo>,</mo> <msub> <mi>d</mi> <mi>e</mi> </msub> </mrow> </msub> </math>  $$ {\mathrm{RQED}}_{d_{\gamma },{d}_e} $$ ) a model describing fermions in a d  e -dimensional space-time and interacting via the exchange of massless bosons in d  γ -dimensions (d  e  ≤ d  γ ). We compute the two-loop mass anomalous dimension, γ  m , in general   <math> <msub> <mtext>RQED</mtext> <mrow> <mn>4</mn> <mo>,</mo> <msub> <mi>d</mi> <mi>e</mi> </msub> </mrow> </msub> </math>  $$ {\mathrm{RQED}}_{4,{d}_e} $$  with applications to RQED4,3 and QED4. We then proceed on studying dynamical (parity-even) fermion mass generation in   <math> <msub> <mtext>RQED</mtext> <mrow> <mn>4</mn> <mo>,</mo> <msub> <mi>d</mi> <mi>e</mi> </msub> </mrow> </msub> </math>  $$ {\mathrm{RQED}}_{4,{d}_e} $$  by constructing a fully gauge-invariant gap equation for   <math> <msub> <mtext>RQED</mtext> <mrow> <mn>4</mn> <mo>,</mo> <msub> <mi>d</mi> <mi>e</mi> </msub> </mrow> </msub> </math>  $$ {\mathrm{RQED}}_{4,{d}_e} $$  with γm as the only input. This equation allows for a straightforward analytic computation of the gauge-invariant critical coupling constant, α  c , which is such that a dynamical mass is generated for α  r  &gt; α  c , where α  r  is the renormalized coupling constant, as well as the gauge-invariant critical number of fermion flavours, N  c , which is such that α  c  → ∞ and a dynamical mass is generated for N &lt; N  c . For RQED4,3, our results are in perfect agreement with the more elaborate analysis based on the resolution of truncated Schwinger-Dyson equations at two-loop order. In the case of QED4, our analytical results (that use state of the art five-loop expression for γ  m ) are in good quantitative agreement with those obtained from numerical approaches.