Local anodic bonding of a common Kovar alloy to Pyrex is presented. This technique is ideally suitable for temperature-, solvent- and pressure-resistant microfluidic connections. In this paper we mainly concentrate on the stress problems occurring during and after bonding. Because of the different thermal expansion coefficients of Kovar and Pyrex a structure is added in order to release the thermal stresses induced during bonding. Optimum bonding conditions in vacuum on Pyrex and on a Pyrex-Si bonded wafer pair are investigated. In the latter case bonding for 3 h at 250 °C and 1.5 kV results in a high-quality bond.