At the end of April 2, 1978, the ISEE 1 and 2 spacecraft moved inbound at approximately 11 R(E) on the nightside (0130 MLT). Due to a flapping motion of the plasma sheet the spacecraft crossed the neutral sheet region (central region of the plasma sheet) more than 10 times in the hour between 2115 and 2215 UT. This provided a unique opportunity to study the structure of the plasma/current region and its evolution during substorm growth and early expansion before the final disruption of the current sheet. Using minimum variance analysis of the magnetic field variations during the crossings as well as finite ion gyroradius diagnostics, we determine the orientation of the current sheet (CS) and then estimate the CS thickness as well as the value of its normal component, B(n). Typically, the current distribution was inferred to be very inhomogeneous with a current concentrated in a very thin CS (only 0.2 to 0.8 R(E) as thick) embedded inside the thicker plasma sheet. Current sheet crossings could be classified as regular or turbulent. The first type prevailed during the growth phase and at the initial stage of expansion when the spacecraft were well outside (in longitude) of the active region of the substorm and no large plasma flow was detected. The normal field component B(n) was typically very small (approximately 1 nT) in the CS center in comparison to the larger shear magnetic B(y) component. In the course of the growth phase we inferred an increase of the lobe field B(x) and a decrease of the CS half thickness h (from h approximately 3000 km to approximately 800 km just before the expansion onset), i.e., a very large increase (up to an order of magnitude) of the current density. At the same time, in disagreement with the usual cartoon picture of magnetic reconfiguration, the magnetic field magnitude in the CS center increased (instead of decreased) at the expense of the shear component. Three turbulent crossings were found during substorm expansion within the longitude range of the substorm current wedge (SCW). The second of them was detected approximately 1 min before the main dipolarization and was characterized by a rather small CS thickness (h <600 km), by strong earthward plasma flow and by a positive normal magnetic field component. That period showed signatures of concentration of both cross-B and field-aligned current at the outer edge of CS and may indicate a nearby reconnection region. The main result of this study is that the region of very thin current sheet (thickness of the order of the gyroradius of thermal protons in the field just outside the current sheet), which contained a very small normal component, clearly appeared in the near tail prior to the sudden onset of current disruption as predicted by some quantitative models of quasi-static evolution of earthward convecting plasma sheet flux tubes. Comparing these observations to theoretical results, we find that the threshold conditions for the growth of the tearing mode instability in sheared magnetic fields were apparently satisfied in this case, but the growth rate was too slow for sudden initiation of substorm expansion.